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mechanics American Academy of Mechanics Academia Americana de Mecanica Volume 31, Number 3-4 March-April 2002 (references in the form \M28(3-4)" indicate the last time the Journal was cited in mechanics: v. 28, n. 3-4, in this case.) Letter from the Editor Position Openings Announcements Selections of the Editor Application for Membership mechanics Contents Acta Materialia Acta Mechanica AIAA Journal Applied Mathematical Modelling Applied Mathematics and Mechanics Applied Mechanics Reviews Archive for Rational Mechanics and Analysis Archive of Applied Mechanics Archives of Mechanics Communications on Pure and Applied Mathematics Composites Part A: Applied Science and Manufacturing Computational Mechanics Computer Methods in Applied Mechanics and Engineering Computers & Fluids Computers & Structures Earthquake Engineering & Structural Dynamics Engineering Fracture Mechanics Engineering Mechanics Engineering Structures European Journal of Mechanics A-Solids European Journal of Mechanics B-Fluids Experimental Mechanics Experiments in Fluids Fatigue & Fracture of Engineering Materials & Structures Finite Elements in Analysis and Design Flow, Turbulence and Combustion IMA Journal of Applied Mathematics Industrial Mathematics International Journal for Numerical and Analytical Methods in Geomechanics International Journal for Numerical Methods in Engineering International Journal for Numerical Methods in Fluids International Journal of Damage Mechanics International Journal of Engineering Science International Journal of Fatigue International Journal of Fracture International Journal of Heat and Fluid Flow International Journal of Heat and Mass Transfer International Journal of Impact Engineering International Journal of Mechanical Sciences International Journal of Non-Linear Mechanics International Journal of Plasticity I II IV XII BC 1 M31(1-2) 1 1 5 5 M28(3-4) 6 7 M26(1) 7 M31(1-2) M30(9-10) 7 8 M31(1-2) 9 M31(1-2) M30(1-2) 10 11 M31(1-2) 11 11 12 M31(1-2) 12 12 M30(5-6) 12 13 15 M31(1-2) 16 M31(1-2) 16 17 17 M31(1-2) M31(1-2) M31(1-2) 17 International Journal of Pressure Vessels and Piping International Journal of Solids and Structures Inverse Problems in Engineering Journal of Applied Mathematics and Mechanics Journal of Applied Mechanics Journal of Biomechanical Engineering Journal of Biomechanics Journal of Composite Materials Journal of Computational and Applied Mathematics Journal of Computational Physics Journal of Elasticity Journal of Engineering Materials and Technology Journal of Engineering Mathematics Journal of Engineering Mechanics Journal of Fluid Mechanics Journal of Fluids and Structures Journal of Fluids Engineering Journal of Intelligent Material System and Structures Journal of Microelectromechanical Systems Journal of Non-Newtonian Fluid Mechanics Journal of Reinforced Plastics and Composites Journal of Sound and Vibration Journal of Strain Analysis for Engineering Design Journal of the Mechanics and Physics of Solids Journal of Thermal Stresses Journal of Vibration and Acoustics Journal of Vibration and Control JSME International Journal Series A JSME International Journal Series B JSME International Journal Series C Mathematics & Mechanics of Solids Meccanica Mechanics of Composite Materials and Structures Mechanics of Materials Mechanics of Solids Mechanics of Structures and Machines Mechanics Research Communications Medical Engineering & Physics Nonlinear Dynamics Prikladnaya Mekhanika Probabilistic Engineering Mechanics Proceedings of the Royal Society of London, Series A, Mathematical, Physical and Engineering Sciences Quarterly Journal of Mechanics & Applied Mathematics Quarterly of Applied Mathematics Rheologica Acta Shock and Vibration SIAM Journal on Applied Mathematics Structural Engineering Earthquake Engineering Structural and Multidisciplinary Optimization Studies in Applied Mathematics Technische Mechanik Theoretical and Applied Fracture Mechanics Thin-Walled Structures Wave Motion Zeitschrift f ur Angewandte Mathematik und Mechanik Zeitschrift f ur Angewandte Mathematik und Physik M31(1-2) M31(1-2) 18 M31(1-2) M31(1-2) M30(9-10) M31(1-2) 18 M31(1-2) 18 19 M30(11-12) 20 20 20 22 M31(1-2) 23 24 24 M30(7-8) 24 27 M31(1-2) 28 M30(11-12) 28 28 M31(1-2) 29 M31(1-2) 30 M31(1-2) 30 M29(5-6) 30 30 M31(1-2) 30 M29(3-4) M31(1-2) 32 33 33 33 M31(1-2) M31(1-2) M28(5-6) M31(1-2) 34 M26(3) M31(1-2) 34 M31(1-2) 34 35 mechanics provides its readers with news in the eld of theoretical and applied mechanics, and serves as a forum for the presentation and discussion of issues related to the development of the science and profession of mechanics. Opinions expressed are those of the authors and do not necessarily reect oÆcial points of views of AAM or the institutions with which the authors are aÆliated. mechanics Editor: Horacio D. Espinosa (Northwestern University, U.S.A.) Gustavo Buscaglia (Balseiro Institute, Argentina), Eduardo Dvorkin (Univ. Nac. de Buenos Aires, Argentina), Robert Haythornthwaite (Temple University, U.S.A), Dean T. Mook (Virginia Tech, U.S.A), Djenane Pamplona (PUC-Rio, Brazil), G. Ravichandran (Caltech, U.S.A). Associate Editors: The American Academy of Mechanics is a non-prot corporation incorporated in 1969 under the laws of the Commonwealth of Pennsylvania. Its objective is to advance the science and profession of mechanics, with particular reference to the countries of North, South, and Central America. It aims to facilitate cooperation among mechanicists, to encourage recognition of achievements in mechanics, and to promote public understanding of the work of the mechanicist. (2001): M. Beatty (University of Nebraska), President and Chairman of the Board; F. Moon (Cornell University), Immediate past President; D.T. Mook (VPI and State University), Secretary; R.A. Heller (VPI and State University), Treasurer; L. Virgin, Director, Region IA (Eastern USA); S. Datta (University of Colorado), Director, Region IB (Central and Western USA); M. Paidoussis, Director, Region II (Canada); P. Kittl (University of Chile, Chile) Director, Region III (Central and South America); R.M. Haythornthwaite (Temple University), Publisher; C.W. Bert (Univ. of Oklahoma), Secretary to the Fellows. Board of Directors (ISSN 0076-5783) POSTMASTER: Send address changes to mechanics, Subscription and Membership, ESM, MC 0219, Virginia Tech, Blacksburg, VA 24061 (Tel. 540-231-6871: Fax 540-231-2290). Editorial and Advertising: Horacio D. Espinosa, Northwestern University, 2145 Sheridan Rd., Evanston, IL 60208-3111 (Tel. 847-467-5989, Fax 847-491-3915). Membership in the American Academy of Mechanics includes the subscription to mechanics. mechanics American Academy of Mechanics Academia Americana de Mecanica I Letter from the Editor May 12, 2002 Dear AAM members, As you may have noticed, a year ago I started a section named “Selections of the Editor.” The idea has been to bring to you information on new technologies, historical notes or as in this issue, articles discussing the future of fast evolving technologies from a business perspective, see “The Future of the Microprocessor Business,” by M.J. Bass and C.M. Christensen, as well as “The Opportunity and Threat of Disruptive Technologies,” by C.M. Christensen. The insight provided by these articles is very valuable in guiding our choice of research endeavors with the potential of having a significant societal impact. I would like to take this opportunity to invite you to contribute to Mechanics with articles written for a general audience addressing important educational developments, historical notes on various aspects of mechanics or other topics you may consider appropriate. The articles should be preferably written in English but this is not a requirement. In fact, this issue contains an article entitled “About the Path to Progress in Buckling Theory,” by L.A. Godoy, which is presented in Spanish. I hope that this editorial decision will encourage more contributions from Central and South American AAM members or readers. Lastly, I would like to bring to your attention a letter I received from Dr. P.P. Nelson, Director of the Civil and Mechanical Systems Division at the National Science Foundation, which is published with her permission. Two issues discussed in her letter deserve special attention from you. The first is the announcement of the retirement of Dr. Jorn Larsen-Basse. I am sure you all will join Dr. Nelson in thanking Jorn for his excellent service and support to our community for the past many years. The second is the announcement of a number of position openings in the CMS Division including the Director position. As you may be aware, some people in the mechanics community have expressed dissatisfaction and frustration with what is perceived as a low funding level in the area of mechanics and as a result a low success rate of proposals submitted to CMS. Although this perception may be argued, I would like to quote a statement by Dr. O. Dillon, which he recently told me in regards to this issue, “… people in mechanics need to get more involved and serve in various capacities at NSF in order to increase recognition of our field’s contributions and its societal impact.” I am sure you will agree with Oscar’s reasoning; hence, I urge you to become involved and submit nominations to Dr. Nelson. Best wishes to all and a special greeting to all the moms in our community. Horacio D. Espinosa Editor II POSITION OPENINGS National Science Foundation Civil and Mechanical Systems (CMS) Division Greetings: I would like to inform the mechanics community that Dr. Jorn Larsen-Basse, who served as a program manager in surface engineering and materials engineering for many years, has informed NSF of his intention to retire at the end of this calendar year. I encourage you to express your appreciation to Dr. Larsen-Basse for his years of service to your community - he has done a wonderful job! At this time, the Civil and Mechanical Systems (CMS) Division has vacancies for Program Managers in the three Program areas, one of which is the 1633 program: • • • The Structural Systems and Hazards Mitigation of Structures (SSHM) Program (1637) The Dynamic System Modeling, Sensing and Control (DSMSC) Program (1632) The Solid Mechanics and Materials Engineering (SMME) Program (1633) The link to the CMS web page is http://www.eng.nsf.gov/cms/ and descriptions of these opportunities can be found through that page. I expect that you know of colleagues who would be good candidates. Please consider and send the names and contact information for those you wish to nominate to me ([email protected], 703-292-7018) or to the CMS Search Coordinator (Dr. Richard Fragaszy, [email protected], 703-292-7011). These positions are not limited to individuals who currently hold academic positions, so think about anyone you might know in industry or in a government job as well as faculty members. The CMS Division needs highly qualified individuals to manage existing programs and to expand the grant opportunities we provide for Civil, Mechanical and related engineering disciplines. We all benefit from having well qualified, enthusiastic staff in CMS. In addition, we are advertising for the important position of George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) Equipment Project Coordinator. This position has been occupied by Dr. Thomas Anderson, and he has informed NSF that he will be leaving this position during this summer after two years of service. We thank Tom for his contributions, and encourage you to consider nominating persons from academe or industry for this very important position. The position of Division Director (currently my position) is also being advertised. We need your help in identifying highly qualified candidates for all of these positions. Please feel free to contact me if you have any questions. Best regards, Dr. Priscilla P. Nelson Director, Division of Civil and Mechanical Systems Directorate for Engineering National Science Foundation 4201 Wilson Boulevard, Suite 545 Arlington, VA 22230 Tel: (703) 292-7018 (direct) or 292-8360 (general) Fax: (703) 292-9053 [email protected] III Civil Engineering School of Engineering and Applied Science Department Chair Position The University of Virginia School of Engineering and Applied Science invites applications for the chairperson of the Department of Civil Engineering. The University of Virginia has approximately 18,000 students pursuing degrees in nine colleges and professional schools, including the School of Engineering and Applied Science (SEAS). The University of Virginia is consistently ranked as one of the top public universities in the country. The School of Engineering and Applied Science has approximately 2,000 undergraduate students, 600 graduate students, 150 tenure and tenure track faculty members in nine departments, and conducts approximately $40 million per year in externally funded research programs. The Department of Civil Engineering has more than 150 undergraduate students, 75 graduate students, and 15 faculty members. The department offers B.S., M.S., M.E., and Ph.D. degrees in civil engineering. The department has undergone significant growth and programmatic evolution. The department is implementing a new undergraduate curriculum, actively expanding its graduate research program, and is engaged in multi-disciplinary programs with other departments, schools, and universities. Active research programs exist within three main thrust areas: environmental and geo-environmental engineering; structural engineering and applied mechanics; and transportation systems, operations, planning, and safety. We seek a chairperson who can provide leadership for a department committed to excellence in teaching, research, and service, guide the growth of new promising directions, and visibly enhance the department’s national stature. Requirements: Candidates must have an earned doctorate in an appropriate discipline and an outstanding record of scholarship and research achievement. Candidates with exceptional credentials will be considered for an endowed professorship. Applications will be reviewed as they are received and until the position is filled. Interested Candidates please submit a letter of application to: Professor James H. Aylor, Search Committee Chair, Ref. #5954, School of Engineering and Applied Science, Dept. of Electrical & Computer Engr., University of Virginia, 351 McCormick Road, P. O. Box 400743, Charlottesville, VA 22904-4743; Email: [email protected]; Phone: 434-924-6100. Applicants are encouraged to visit the departmental website for more information at: http://www.cs.virginia.edu/~civil/. The University of Virginia is an equal opportunity, affirmative action employer. IV ANNOUNCEMENTS AAM AWARDS NOMINATIONS The Awards Committee of the American Academy of Mechanics requests nominations for the following two awards to be presented at the upcoming ASME International Mechanical Engineering Congress and Exposition in November, 2002 The 2002 American Academy of Mechanics Outstanding Service Award Preliminary nominations should consist of a one-page letter describing the outstanding service of the nominee to the Academy as well as to the profession, along with a one- page biographical sketch of the nominee, together with the names of at least three people willing to write letters of support in the event that the Awards Committee requests them. The 2002 American Academy of Mechanics Junior Award This award, which will be based primarily on research accomplishments, is open to mechanicians whose highest degree was conferred after December 31, 1991. Preliminary nominations will consist of a one-page nominating letter, one-page curriculum vitae, and re(or pre-) prints of the candidate’s best three papers. In the case of co-authorship of any work submitted, the candidate’s contribution must be clearly and explicitly indicated in an attached note. Please Note: * All preliminary nominations for both awards must be postmarked by August 1, 2002. Those that do not arrive in a timely fashion will not be considered. Once the preliminary materials are reviewed, additional biographical and complete dossiers may be requested of applicants under consideration. For additional information, please do not hesitate to contact Simon Ostrach at [email protected] or Stephen Crandall at [email protected], who are current members of the awards committee. AAM Awards Committee Simon Ostrach, Chair, Stephen Crandall, Tinsley Oden, Wolfgang Knauss, Romesh Batra * Please note change in submission date from previous years. V NOMINATIONS FOR FELLOW OF THE AMERICAN ACADEMY OF MECHANICS NOTES: • Persons nominated must be members of the Academy (Bylaws, III 1). • Nominations must be made by two of the Fellows (Bylaws, III 2). • Fellows shall be elected on the basis of their contributions to mechanics (Bylaws, III 1). Name of the member nominated (please print) Citation (please state in no more than fifteen words the basis of the nomination) Nominated by (signatures of two fellows required) Signature: Printed Name: Date: Signature: Printed Name: Date: Please mail this nomination form (no faxes please!) to: Professor C. W. Bert School of Aerospace & Mechanical Engineering The University of Oklahoma Norman, Ok 73019-1052, USA so as to reach him on or before September 24, 2002. The nomination should include one good copy of a two-page resume of the member nominated. VI American Academy of Mechanics Founders Prize and Grant Up to $10,000 For the Academic Year 2002-2003 (Deadline: July 1, 2002) The American Academy of Mechanics is pleased to announce the availability of a Founder’s Prize and Grant to be awarded in September 2002 to a doctoral candidate in the field of Mechanics. Funding has been arranged by the Robert M. and Mary Haythornthwaite Foundation through the good offices of Professor Haythornthwaite, founder and first President of the Academy. The aware will be made on the recommendation of an AAM committee. The prize consists of a Certificate and $1,000 that will be presented at the annual meeting of the Academy, usually held in November. The Grant will be made to that same person in two installments, $6,000 in September 2002 and up to $3,000 in January 2003, the latter dependent on the size of the approved budget and receipt by the AAM committee of an acceptable progress report. In order to encourage contestants to think constructively about the impact of new and pending developments, they will be asked to compose an original essay of no more than a thousand words under the title “Progress through Mechanics”. The winning essay will be published in mechanics. The award is open to those who, as of July 1, 2002, are registered as graduate students at a degree granting institution within the Americas, have completed at least one year of full-time graduate study at that institution, have been assigned a thesis advisor at the institution and have had a doctoral thesis topic emphasizing mechanics approved by the institution following candidacy or equivalent procedures. There are no restrictions with regard to citizenship, residency, race, religion, or sex. Letters of support will be required of the thesis advisor and in addition one from either a Member or a Fellow of AAM. Contestants will be judged on the basis of the essay, plans, references and academic history. The intent of the Grant is to support the research of the student through an approved combination of equipment purchases, information access, travel, etc., but not routine living expenses or fees. Detailed rules for the competition will be issued soon: to receive them, express your interest to the committee by FAX to (215) 204-6936, or by writing to: AAM Founders Prize and Grant Committee c/o Civil and Environmental Engineering Department Temple University (084-53) Philadelphia, PA 19122 VII PACAM VIII Eighth Pan American Congress of Applied Mechanics January 5-9, 2004 Havana, Cuba http://www.pacam8.mcgill.ca/ The Eighth Pan American Congress of Applied Mechanics (PACAM VIII), jointly sponsored by the University of Havana, the Institute of Cybernetics, Mathematics, and Physics of Cuba, and the American Academy of Mechanics, will be held January 5-9, 2004 at the Convention Center, Havana, Cuba. The Honorary Chairman of the Organizing Committee is Prof. Alina Ruiz Jhones of the University of Havana. The Co-Chairmen are Prof. Martin Ostoja-Starzewski of McGill University and Prof. Reinaldo Rodríguez-Ramos of the University of Havana. The Chairman of the Editorial Committee is Prof. Julián Bravo-Castillero of the University of Havana, and the Chairman of the Local Arrangements Committee is Prof. Raúl Guinovart-Diaz of the University of Havana, Cuba. The aim of sponsors is to promote progress in the broad field of mechanics by (1) exposing engineers and scientists, including graduate students, to new research findings, techniques, and problems, and (2) providing opportunities for personal interactions between mechanicians of North and South America, as well as other continents. It is the only conference sponsored by the American Academy of Mechanics (AAM). The Pan American Congresses of Applied Mechanics are held every two years early in January, always in a Latin American venue, at a time when few other conferences are scheduled. The previous Congresses were held in Rio de Janeiro, Brazil in 1989; Valparaiso, Chile in 1991; São Paulo, Brazil in 1993; Buenos Aires, Argentina in 1995; San Juan, Puerto Rico in 1997, Rio de Janeiro, Brazil in 1999 and Temuco, Chile in 2002. Participants come from the Americas as well as Africa, Asia, Australia, and Europe. Persons willing to organize special sessions in any area of mechanics are welcome to contact the organizers listed below. All the future announcements will be made at the website listed above, and through the AAM (http://www.AAMech.org/). Four-page papers for the conference proceedings will be due June 30, 2003, at either address: Latin American Co-Chairman Prof. Reinaldo Rodríguez-Ramos Facultad de Matemática y Computación Universidad de la Habana San Lazaro y L, Vedado, CP 10400 La Habana, Cuba [email protected] http://www.uh.cu North American Co-Chairman Prof. Martin Ostoja-Starzewski Department of Mechanical Engineering McGill University 817 Sherbrooke Street West Montréal, PQ, Canada H3A 2K6 [email protected] http://www.mcgill.ca VIII International Symposium on Dynamic Problems of Mechanics (X-DINAME) Dynamics of the Brazilian Society of Mechanical Sciences 10-14 March, 2003 Hotel Recanto das Toninhas Ubatuba, São Paulo Call for Abstracts Abstract Criteria: Abstracts of scientific works are invited in all dynamic problems of mechanics. The work should be original in scope, of outstanding quality and of permanent interest. Abstracts are invited in the following topic areas: • Structural and machine dynamics • Control and optimization • Noise and vibration • Modal analysis • Any other correlated subject. Information about the meeting: The meeting is to take place on the week 10-14th of March, 2003 at Hotel Recanto das Toninhas (http://www.toninhas.com.br), Ubatuba, São Paulo. Ubatuba is located somewhere in between Rio and São Paulo, in one of the most attractive and exuberant coastal areas of Brazil, with a consistent touristic structure of hotels and restaurants. It is adjacent to the preservation sanctuary of the Atlantic Ridge Rain Forest and beautiful tropical beaches. The hotel, which is a resort by the sea, provides the right kind of welcoming atmosphere and international standards service which is required for the immersion activities of DINAME. Since the hotel has a limited number of apartments early booking is encouraged. Key Deadlines: April 30, 2002: Last day for submission of abstracts for preliminary evaluation of contributions. May 24, 2002: Notification of selected abstracts and invitation for submission of full texts. July 31, 2002: Last day for receiving full texts. August 30, 2002: Notification of accepted papers and/or required modifications of the text. September 30, 2002: Last day for receiving modified texts. January 15, 2003: Last day for confirming early booking with the hotel. A home page for the conference is to become available soon. Any additional information can be obtained by writing to the following address: [email protected] IX IUTAM Symposium On Integrated Modeling of Fully Coupled Fluid-Structure Interactions Using Analysis, Computations, and Experiments 1 June-6 June 2003 New Brunswick, New Jersey USA http://cronos.rutgers.edu/~mechaero/iutam Chairs: • Haym Benaroya and Timothy Wei, Rutgers University, New Jersey [email protected] and [email protected] Scientific Committee • Peter Bearman, Imperial College of Science, Technology and Medicine, UK • Earl Dowell, Duke University, North Carolina • Helmut Eckelmann, Georg-August-Universität, Germany • Peter Monkewitz, IMHEF-EPFL, Switzerland • Michael Païdoussis, McGill University, Canada • John Sheridan, Monash University, Australia • H.K. Moffatt, Isaac Newton Institute for Mathematical Sciences, UK This Symposium will provide a forum for the latest thinking in analytical, computational and experimental modeling of structures interacting with fluid environments. The specific objective is to provide a structured format in which meaningful and lasting dialogues can be facilitated between leading researchers in the different component disciplines. It is intended that, through these dialogues, multidisciplinary linkages will be established leading to integrated approaches to modeling the complex, nonlinear interactions between fluids and structures. Examples of classes of interactions that may be addressed in this Symposium include ocean structures, fluid conveying structures, and aerospace structures. The energy transfer processes are inherently nonlinear in all aspects of the behavior. The important class of vortex-induced oscillations has regions of lock-in, where the structural natural frequencies rather than the fluid velocity govern the shedding, and there exists hysteretic behavior. The real fluidstructure system is one of complex exchanges of forces and energies, resulting in highly nonlinear behaviors. The ability to model, solve and test fully coupled fluid-structure systems portends a rich and profound understanding. In fact, recent research efforts have indeed started to focus on the development of fully coupled models. This Symposium is therefore a response to these new and exciting developments in the field. By bringing together a critical mass of key researchers in each discipline, and organizing the program to focus on multidisciplinary problem solving, this process of developing fully coupled fluid-structure interaction research programs can be reinforced and enhanced. We look forward to receiving abstracts for review, presentation, and eventual full publication, of topics that fall within the broad framework defined above. DEADLINES Submission of Abstracts: 1 February 2003 Notification of Acceptance: 15 March 2003 Hotel & Symposium Registration: 1 May 2003 Symposium: Sunday 1 June – Friday 6 June 2003 Final Manuscripts Due: Friday 13 June 2003 (FIRM) X FOURTH INTERNATIONAL SYMPOSIUM ON VIBRATIONS OF CONTINUOUS SYSTEMS The Fourth International Symposium on Vibrations of Continuous Systems will take place in Keswick, England, July 7-11, 2003. The primary goal of this Symposium is to bring together outstanding experts in the field of vibrations of continuous systems from all over the world, to discuss technical topics in a very informal atmosphere. As before, participation will be by invitation only, and will be limited to maximum numbers of 50 participants and 40 presentations. The Symposium is devoted to the vibrations of continuous systems (e.g. strings, rods, straight and curved beams, membranes, plates, shells, and three-dimensional bodies). Examples of topics to be considered include: free and forced vibration, linear and nonlinear vibration, undamped and damped vibration, fluid-structure interaction, and structural elements of composite material. The Symposium location, Keswick, is in the heart of the Lake District of northwestern England, famous for its beautiful lakes and hills. Typical days at the Symposium will consist of morning hikes or bus excursions, presentation sessions in the afternoons, and social gathering times in the evenings. The outings and social gatherings have proved to be excellent ways of generating relaxed and informal technical discussions and friendships which have been of great value to ongoing research. Individuals who are interested in taking part in this Symposium should write to: Professor Arthur W. Leissa General Chairman, ISVCS IV Dept. of Mechanical Engineering 206 West 18th Ave. Ohio State University Columbus, Ohio 43210 USA Letters should be accompanied by a one-page summary of the writer’s research accomplishments (include a list of published books, papers, reports, etc.) in the theme of this Symposium. AAM Annual Business Meeting The Annual Business Meeting of the American Academy of Mechanics will be held on Thursday, June 27, 2002, in conjunction with the 14th USNCTAM Meeting (June 23-28, 2002) at the Virginia Polytechnic Institute and State University at Blacksburg. The conference banquet will be held in the evening from 7:00 p.m. to 10:00 p.m. Plan now to participate in the AAM business meeting. The Board of Directors will meet 11:30 a.m. to 1:30 p.m. for a working luncheon. The Secretary will issue an agenda within thirty days prior to the Board Meeting. The Fellows Meeting will convene from 1:30 p.m. to 2:30 p.m. At this time, the President-Elect presiding and in accordance with Bylaw Article III.3: “The Fellows shall elect one of their number as Secretary to the Fellows.” The term of office shall be from three to five years, to be specified. The General Members Meeting will be held from 2:30 p.m. to 3:30 p.m. XI CALL FOR NOMINATIONS FOR DIRECTOR OF REGION IB, CENTRAL AND WESTERN USA Nominations are called for Director of Region IB, Central and Western USA, for a three-year term of service commencing in June 2003. The nominee must be an active Member of the Academy registered in that region; and nominations shall be accepted only from active Members resident in that region. Valid nominations must bear the signatures of five (5) Members of the Academy who are residents of the region and are Members in good standing. Nominations shall include a letter from the nominee accepting the nomination. The deadline for submissions is September 30, 2002. Early nominations are strongly encouraged. Please submit all nominations to Professor Dean Mook, Secretary American Academy of Mechanics Department of Engineering Science and Mechanics Virginia Polytechnic and State University Blacksburg, VA 24061-0219 CALL FOR NOMINATIONS FOR DIRECTOR OF REGION III, CENTRAL AND SOUTH AMERICA Nominations are called for Director of Region III, Central and South America, for a three-year term of service commencing in June 2003. The nominee must be an active Member of the Academy registered in that region; and nominations shall be accepted only from active Members resident in that region. Valid nominations must bear the signatures of five (5) Members of the Academy who are residents of the region and are Members in good standing. Nominations shall include a letter from the nominee accepting the nomination. The deadline for submissions is September 30, 2002. Early nominations are strongly encouraged. Please submit all nominations to Professor Dean Mook, Secretary American Academy of Mechanics Department of Engineering Science and Mechanics Virginia Polytechnic and State University Blacksburg, VA 24061-0219 XII SELECTIONS OF THE EDITOR The Future of the Microprocessor Business Reprinted with permission from Spectrum Vol. 39, No.4, April 2002 By Michael J. Bass and Clayton M. Christensen In a century in which technology left few aspects of life unchanged in some countries, the microprocessor may have been the most transformative of all. In three decades it has worked itself into our lives with a scope and depth that would have been impossible to imagine during its early development. If you live in a developed country, chances are good that your household can boast of more than a hundred microprocessors scattered throughout its vehicles, appliances, entertainment systems, cameras, wireless devices, personal digital assistants, and toys. Your car alone probably has at least 40 or 50 microprocessors. And it is a good bet that your livelihood, and perhaps your leisure pursuits, require you to frequently use a PC, a product that owes as much to the microprocessor as the automobile owes to the internal combustion engine. Throughout most of its history, the microprocessor business has followed a consistent pattern. Companies such as Intel, Motorola, Advanced Micro Devices, IBM, Sun Microsystems, and HewlettPackard spend billions of dollars each year and compete intensely to produce the most powerful processors, which handle data in 32- or 64-bit increments. The astounding complexity and densities of 2 transistors on these ICs—now surpassing 200 million transistors on a 1-cm die—confer great technical prestige on these companies. The chips are used in PCs, workstations, and other systems that, for the most part, have been lucrative, high-volume markets. As with other ICs, microprocessors have for the past few decades been undergoing the exponential rise in performance prophesied by Moore's Law. Named for Intel Corp.'s cofounder, Gordon E. Moore, it describes how engineers every 18 months or so have managed to double the number of transistors in cutting-edge ICs without correspondingly increasing the cost of the chips. For microprocessors, this periodic doubling translates into a roughly 100 percent increase in performance, every year and a half, at no additional cost. The situation has delighted consumers and product designers, and has been the main reason why the microprocessor has been one of the greatest technologies of our time. In coming years, however, this seemingly unshakable industry paradigm will change fundamentally. What will happen is that the performance of middle- and lower-range microprocessors will increasingly be sufficient for growing—and lucrative—categories of applications. Thus microprocessor makers that concentrate single-mindedly on keeping up with Moore's Law will risk losing market share in these fastgrowing segments of their markets. In fact, we believe that some of these companies will be overtaken by firms that have optimized their design and manufacturing processes around other capabilities, notably the quick creation and delivery of customized chips to their customers. The changes portend serious upheaval for microprocessor design, fabrication, and equipmentmanufacturing firms, which have been laser-locked on Moore's Law. Executives lose sleep over whether they can keep on shrinking line widths and transistors and fabricating larger wafers. We don't blame them, given their history. Nor do we see blissfully peaceful slumber in their near future: this is not another article forecasting the imminent demise of Moore's Law. On the contrary, we believe that the top IC fabricators will have little choice but to invest ever more heavily so as to keep on the Moore trajectory, which we expect to go on for another 15 years, at least. We don't see these investments as sufficient for future success, however. XIII Will semiconductors hit a physical limit? They surely will, someday. But this is probably the right answer to the wrong question. The more important question is: as technological progress surpasses what users can use, how do the dynamics of competition begin to change? Bottom to top The stakes are high. The microprocessor market, which totals about US $40 billion a year, has several main tiers. At the top are the most powerful chips, which are used in servers and workstations. Then there's the PC market, dominated by Intel microprocessors. These relatively high-end chips were a major component of a category that rang up US $23 billion in 2001, after peaking at $32 billion the year before, according to the Semiconductor Industry Association (San Jose, Calif.), a trade group. Microcontrollers were another important category, with sales totaling $10 billion in 2001. They are generally less computationally powerful than high-end microprocessors, and exert real-time control over other systems, such as automobile engines. Finally, digital signal-processing chips, a key component of cell phones, DVD players, and other entertainment products, had sales of $4 billion last year. With their exponentially increasing performance, microprocessors might seem unique and unlikely to follow the broad evolutionary pattern that has played out in the past in most other technology-based industries. After all, the Moore's Law phenomenon is unprecedented in industrial history. But strong evidence shows that the same evolutionary pattern that occurred in mainframe computers, personal computers, telecommunications, banking, hospitals, and steel production is indeed occurring in the microprocessor business. The pattern begins with a stage in which available products do not yet perform up to most customers' needs. So, not surprisingly, companies compete by making better products. In other words, competition during this stage is basically driven by performance. As engineers design each successive generation of product, they strive to fit the pieces together in ever more efficient ways to wring the most performance possible out of the technology available. Typically, major subsystems need to be interdependently designed—and, as a result, a competitor needs to make all the product's critical subsystems. During this phase, the competitive advantage of vertical integration is substantial, so manufacturers do almost everything themselves. This is the way it was in the earliest days of the PC industry, for example. The next stage of an industry's development begins when the performance of its products has overshot the needs of customers in the less-demanding tiers of the market. These customers won't pay premium prices for more performance, of course, but will pay extra for a product that is extraordinarily reliable, or one that has been customized to meet their specific needs—especially if they can get that ultra-reliable or customized product quickly and conveniently. Ease of use is another feature that customers typically reward with a premium. To compete on the dimensions of customization, quick delivery, and convenience, product architectures whose pieces are strongly technologically interdependent tend to give way to modular ones, in which the interfaces among subsystems are standardized. This modularization lets designers and assemblers respond quickly to changing customer requirements by mixing and matching components. It also lets them upgrade certain subsystems without redesigning everything. But perhaps the most important repercussion of modularization is that it usually spurs the establishment of a cadre of focused, independent companies that thrive by making only one component or subsystem of the product. Think Seagate Technology in hard-disk drives, or Delphi Delco in automotive electrical systems. One of us (Christensen) has studied how industries that are in transition between the two stages present peril for established firms—and opportunity for upstarts. Large firms can easily become blind to shifts in the types of performance that are valued. For an established company, with its well-defined competencies and business models, the obvious opportunities for innovation are those that focus on unsatisfied customers in the higher market tiers. After all, that is where the innovations that the company has structured itself to deliver are still being rewarded by premium prices. XIV Inevitably, though, this high-tier, performance-hungry group of customers shrinks as performance gets better and better. At the same time, in lower market tiers there is a huge increase in customers who are willing to back off from the leading edge of performance in exchange for high reliability, customization, ease of use, or some combination of all three. Too much of a good thing? This is precisely the juncture at which the microprocessor market has now arrived. Price and performance, fueled by the industry's collective preoccupation with Moore's Law, are still the metrics valued in essentially all tiers of the market today. Even so, there are signs that a seismic shift is occurring. The initial, performance-dominated phase is giving way to a new era in which other factors, such as customization, matter more. Perhaps the best evidence that this shift is under way is the fact that leading-edge microprocessors now deliver more performance than most users need. True, emerging applications like three-dimensional games, the editing of digital-video files, and speech-to-text tax the fastest available microprocessors. However, few people who regularly run such applications do so on a single-microprocessor PC. And that fact is unlikely to change. In the future, as now, many of these taxing applications will run on specialpurpose or separate processors. Hundreds of Athlon microprocessors, from Advanced Micro Devices, are fabricated on 200-mm wafers at a new plant in Dresden, Germany [above]. Though designed for PCs, the 1-GHz chips perform beyond the levels most PC users need. MATTHIAS RIETSCHE/AP PHOTO In any case, the users who run these applications regularly are few compared to the masses who use their PCs mainly for word processing, scheduling, e-mail, and Internet access. For this majority, high-end microprocessors—Intel's Itanium and Pentium-4, and Advanced Micro Device's Athlon—are clearly overkill. Running common benchmark programs, these chips can perform more than one billion floatingpoint operations per second (flops), and in some cases, more than 2 gigaflops. Yet, Microsoft's Windows XP, the most recent version of the ubiquitous operating system, runs fine on a Pentium III microprocessor, which is roughly half as fast as the Pentium-4. What will the microprocessor business be like after this shift? Consider how the PC business grew from a cottage industry into a global colossus over the past 25 years. In the early days, the 1970s, vertically integrated companies such as Apple Computer, Tandy, Texas Instruments, Commodore, and Kaypro built their computers around proprietary architectures and generally wrote their own software. Then, in 1981, IBM shook up the industry with its original PC, which had a modular architecture and subsystems built by such suppliers as Intel, Microsoft, and Seagate. Early on, Apple's products were by consensus the best-performing and most reliable in the industry. But in time, as microprocessors, software, and other key components improved, garden-variety PCs became good enough for mainstream applications like word processing and spreadsheets. Competitive advantage shifted to the nonintegrated companies whose products made use of IBM's modular architecture. These were the clone makers—Compaq, Packard Bell, Toshiba, AT&T, and countless others. Not long after XV that, dependability became the central axis of competition, and a few firms with reputations for reliability— IBM, Compaq, and Hewlett-Packard—managed to command price premiums. By the early to mid-1990s, functionality and reliability had become more than good enough from just about everyone, and the way that computer makers needed to compete shifted again. This change set the stage for Dell Computer Corp. (Round Rock, Texas) to rocket from the lowest tiers of the market to industry dominance. Dell let consumers in their homes or offices specify a set of features and functions for their computer to meet their particular needs. Dell then delivered that computer to their door in a few days. In effect, by coming up with a business model that emphasized customization, speed of delivery, and convenience, Dell pushed the industry into its next stage of development. Although our example is PCs, other technology-based industries have evolved similarly, from automobiles to mainframes. In every case, the primary dimension of competition migrated from an initial focus on performance to reliability, convenience, and customization. When performance began exceeding what customers in a tier of the market could use, competition redefined the types of improvement for which those customers would pay extra. Further, the types of features that let suppliers demand premium prices shifted predictably from performance to reliability, convenience, and so on. As this happened, moreover, competitive advantage moved from companies that were highly integrated to ones that were not. Why don't microprocessor makers simply start producing lower-performance chips? A few years ago, Intel Corp. (Santa Clara, Calif.) began doing just that with its Celeron microprocessor. The problem is that Celeron is a one-size-fits-all proposition. Its architecture isn't more modular than that of the Pentium products it is displacing, and it cannot be customized nearly as much as emerging alternatives. Interestingly, while the latest microprocessors offer higher processing rates than most users need, semiconductor fabrication facilities now offer circuit design teams more transistors than they need[see figure]. Put another way, the rate at which engineers are capable of using transistors in new chip designs lags behind the rate at which manufacturing processes are making transistors available for use. This so-called design gap has been widening for some time. In fact, the National Technology Roadmap for Semiconductors noted it five years ago, observing that while the number of transistors that could be put on a die was increasing at a rate of about 60 percent a year, the number of transistors that circuit designers could design into new interdependent circuits was going up at only 20 percent a year. Microprocessors hundreds of times as powerful as today's should emerge from chip-making equipment using extreme ultraviolet radiation. Sandia National Laboratories unveiled such equipment a year ago [above]. PAUL SAKUMA/AP PHOTO The fact that microprocessor designers are now "wasting" transistors is one indication that the industry is about to re-enact what happened in other technology-based industries, namely, the rise of customization. Keep in mind that in order to develop a modular product architecture with standardized interfaces among subsystems, it is necessary to waste some of the functionality that is theoretically possible. Modular designs by definition force performance compromises and a backing away from the bleeding edge. XVI Core customization A form of customization has already taken hold in the lower tiers of the microprocessor industry. Systemon-a-chip (SoC) products are modular designs constructed from reusable intellectual property (IP) blocks that perform specific functions [see "Crossroads for Mixed-Signal Chips," IEEE Spectrum, March 2002, pp. 38-43]. IP blocks vary in size and complexity, ranging from simple functions such as an RS-232 serial port interface or a DRAM memory controller, to a complex subsystem, such as an entire 32- or 64-bit microprocessor. These IP blocks can be used within multiple designs within a company, or used in designs at different firms. In the lower market tiers, several firms are bundling IP blocks into both soft cores (software-like descriptions of the IP blocks that can be synthesized into hardware designs) and hard cores, that is, preverified hardware designs. Such cores range from hundreds of thousands to a few million transistors, and their availability in the marketplace enables firms to focus less on new design and more on system integration. They can select and integrate microprocessor and other types of cores into SoC designs that are then manufactured as special-purpose components for a specific product. Recently, a few companies have been pushing this trend toward component selection and integration even further, into microprocessor cores themselves. Using special design tools, engineers can specify such a microprocessor, and in some cases completely design one, in weeks rather than months. The Impact of Disruptive Technology As the performance of conventional microprocessors improves [red line], they first meet and then exceed the requirements of most computing applications [dotted lines]. Initially, performance is key [blue area]. But eventually, other factors—reliability, time-tomarket, convenience, and customization—become more important to the customer [green area]. And when a disruptive technology [orange line], such as customizable processor cores, is introduced, it inevitably takes over market share from performance leaders. Leading companies in this so-called customizable core movement include Tensilica, ARC Cores, HewlettPackard, and STMicroelectronics. They have a similar philosophy, but target different markets and application needs. The Tensilica Xtensa processor, for instance, offers customization within the XVII framework of a simple microprocessor core. Customers can specify their own instruction set extension by accessing a Web site and using a high-level language, such as Verilog. ARC Cores' ARCtangent family targets the digital signal processor markets. Like Tensilica, it allows users to customize both processor features (bus widths, cache sizes, and so on) and instructions. HewlettPackard's HP/ST Lx family is aimed at scalable multimedia acceleration using Very Long Instruction Word (VLIW) techniques. It lets customers choose the amount of instruction-level parallelism—in other words, how many functional units to include, and how many operations can be performed in parallel. Intel's dilemma So what will happen in the microprocessor market as a whole? It will be a repeat of what has already happened in other technical industries. The trends of customization and speed-to-market will continue to take hold in the lower tiers—in digital signal processing (DSP) and in processors that are embedded within such products as MP3 players, digital cameras, and set-top boxes. Increasingly, sales of standalone digital signal-processing and embedded chips will give way to SoCs that incorporate DSP or other functions. Gradually, over a period of years, the trend will creep upward into higher tiers of the market, including PCs [see graph]. In fact, companies such as SuperH, MIPS Technologies, and ARM already produce reduced-instruction-set microprocessor cores that can be combined on a single die with other functional units, and that are easily powerful enough to serve as a PC's central processing unit. Engineers can specify a microprocessor and in some cases completely design one in weeks, rather than months For high-end companies such as Intel, the dilemma will be that their best and most profitable customers will continue to need exactly the sort of general-purpose, leading-edge processors that Intel is so good at designing and delivering. Nevertheless, broad trends in electronics suggest that growth will increasingly stem from applications in the lower tiers. For example, sales of PCs, the largest market for high-end microprocessors, declined in 2001 for the first time since 1985, according to market research firm Gartner Dataquest (Stamford, Conn.). Meanwhile, although the market for DSPs shrank even more than the rest of the microprocessor category last year, on the whole they have been one of the fastest-growing segments of that category. The growth has been fueled by such up-and-coming sectors as wireless communications, handhelds, and game, music, video, and other entertainment systems. Custom Chips and Future Fabs As custom-configured chips carve out a larger portion of the microprocessor market, major changes are in store for the way chip fabrication facilities operate. To understand why, consider the underlying trends. One is the ever-increasing abundance of XVIII transistors on a chip, which portends a day when the number of chips per product will approach one. Also every chip will, to some degree, be custom-tailored to its application, and product life cycles will be short. Put those trends together and the inescapable conclusion is that, in the foreseeable future, chips will have to be made in a few days, not weeks, as they are now. To achieve that kind of speed, chip fab plants must operate differently, starting with the way wafers flow through them. The dies are fabricated in batches on round semiconductor wafers about the size of a dinner plate [photo]. In today's fabs, those wafers are also produced in batches. Therein lies the problem: as these groups of wafers move from station to station in the fab plant, they have to wait until an entire batch is complete before going on to the next station. At any given time, large amounts of valuable product are simply sitting around the plant. In the future, wafers will need to move rapidly, one by one, through these plants. The difficulty will be finding a way to implement this single-wafer processing in a variety of fabs, all of which have their own proprietary architecture. To our knowledge, no firm as yet has figured out how to do this, though Taiwan Semiconductor Manufacturing Co. (Hsinchu) and United Microelectronics Corp. (Taipei) have made significant progress in this direction. Single-wafer processing will also probably compromise the economic viability of investments in 300-mm wafer-processing equipment. The reason is that, in the past, when a factory converted to a low-inventory process flow (such as single-wafer processing), the effective capacity of that plant typically doubled. What this means for fab plants is that it makes more economic sense to convert a 200-mm-wafer fab plant to single-wafer processing, rather than build a 300-mm-wafer fab plant. The 200-mm, single-wafer-processing fab plant could be expected to process twice the number of wafers per month and therefore as many die as the 300-mm fab—and to do so at much lower levels of cost and complexity. —M.J.B. & C.M.C. Implications, implications If the microprocessor market does become dominated by multitudes of targeted chips produced in relatively small numbers, several intriguing ramifications could develop. First, for chip-makers, time to market will matter much more [see "Custom Chips and Future Fabs"]. Second, as firms target smaller, more specific markets, they will differentiate their products more by discovering specific needs that general-purpose products do not address. This discovery process works better when products are introduced faster and more frequently, in response to feedback from customers. Tensilica, for one, now boasts that new microprocessor cores used within a system-on-a-chip design can be created and their performance tested through simulation in two weeks. The manufacturing latency of most chip fabrication facilities, on the other hand, remains as high as 10 weeks. With product life cycles approaching a year or less, some microprocessors currently spend a good part of their lives being manufactured. In the future this situation will be competitively intolerable. In coming years, success in the microprocessor business will increasingly demand that companies: • Adeptly use modular designs that reuse and recombine silicon intellectual property. • Include multiple circuit types and possibly process technologies on a single die, creating customtailored systems-on-a-chip. • Shrink the design cycle for microprocessors and systems-on-a-chip and dramatically reduce manufacturing latency times (time spent in the plant). • Tolerate, both technically and economically, a manufacturing mix composed of a multitude of lowvolume runs of narrowly targeted products with short market windows. The evolution toward this future will not be driven by or grounded in the choices of managers in today's industry-leading companies. Competition in the relevant tiers of the market will force these new trajectories of improvement to become critical. The only question is which companies will have developed the capabilities and organizational structures required to thrive in these markets. XIX The Opportunity and Threat of Disruptive Technologies Reprinted with permission from MRS Bulletin Vol. 27, No.4, pp. 278-282, April 2002 By Clayton M. Christensen The following article is an edited transcript of the plenary presentation given by Clayton M. Christensen (Harvard Business School) at the 2001 Materials Research Society Fall Meeting on November 26 in Boston. Introduction I am honored to be with you today. I will give context for where the puzzles developed that have led to the research that I summarized in the book The Innovator’s Dilemma. Companies that at one point were very successful and widely admired, fell from their leadership position within 5 to 10 years. This was very poignant for minicomputer companies, for example, which collapsed after their peak in the world economy during the 1970s and 1980s. While the companies were thriving, the business press attributed their successes to the abilities of their management teams. However, when these companies began to quickly unravel around 1988, the business press attributed their failures to the ineptitude of the very same management teams that had been in place during the years of success. I wondered how good managers could get that bad that fast. I was also suspicious because the minicomputer companies fell in unison. It was not just Digital, but also Data General, Prime, Wang, and Nixdorf. While the companies could have colluded on price, they would never have colluded to collapse together. Something more fundamental had to be happening. Oddly, I found that the reason these companies failed, not just in the computer industry, but over and over again in a variety of industries, is that they were well man-aged. The Disruptive Technology Model Certain paradigms of good management that we teach in business schools sow the seeds of a company’s eventual failure. Figure 1 presents a model that consists of three elements. The performance of a product or service is plotted over time. The first element of the model, represented by the dotted line, shows a trajectory of improvement that customers can absorb or utilize over time. This line represents the median in every market. At the high end of every market, customers are very demanding and will never be satisfied with the best products available. At the low end are customers who can be satisfied by very little. The steeply sloping lines of the figure represent a distinctly different trajectory of improvement in the market. They rep-resent the improvement that innovators make available as, generation after generation, they introduce new and improved products. This trajectory of technological progress almost invariably outstrips the ability of customers to utilize those improvements; companies can almost always innovate faster than people’s lives can change to fully utilize those innovations. In pursuing more profitable customers who will pay higher prices for better products in more demanding tiers of the market, companies are prone to over-shoot what the original set of customers is able to utilize at a later point in time. For example, in the mid-1980s when we were first learning to do word processing on those early personal computers, it was not uncommon for us to have to stop our fingers and wait for the Intel 8088 processor to catch up with us. But as Intel has pursued more profitable customers, to whom it could sell better products for higher margins, it has way-overshot what customers in the mainstream of the business computing market are able to utilize. What this also means is that technology that is initially not good enough to be embraced by customers in the mainstream of the market can improve at such a rapid rate that it later intersects with the needs of mainstream customers. XX The third piece of the model relates to “disruptive technology,” which refers to technology that initially underperforms the incumbent technology, but typically offers more flexibility, convenience, or a lower price. A disruptive technology can serve to create new markets, but it can also upset the equilibrium of companies with good reputations and good products. Disruption in Action Computer Industry: From Disk Drives to Intel I initiated my study of what was driving the failure of some groups of firms with the disk drive industry. In five of six product generations in the industry, a new company would enter and rise to the top only to be toppled by another company that entered and rose to the top. I wanted to develop a model that would explain this phenomenon, which I could then apply to other industries. The disk drive industry served as the “fruit fly” in which it was possible to study many “generations” quickly. Through this process of the disk drive study, we built a database of every model of every disk drive introduced in the industry’s history. For each of the products, we obtained data on each of the components that was used in the drive. This allowed us to locate the point in the industry’s history at which each new technology was first used. In this process, we identified 116 distinctly different new technologies. Of the 116, 111 sustained the trajectory of performance improvement in the market, as it existed at the time. In other words, the purpose of the technology was to make a good product better. Of these 111 sustaining technologies, a good number were the simple, year-to-year engineering advancements expected of good companies. Additionally, a remarkable number were truly breakthrough innovations that made good products much better, as depicted in Figure 1. What was interesting is that it did not matter technologically how difficult the innovation was. In all 111 of these cases, 100% of the time, the companies that led the industry in developing and adopting the new technology had been the leaders of the old technology. As long as the innovation enabled the company to make a better product that they XXI could sell for higher margins to their best customers, it was on management’s radar screen and it received the necessary resources to get it done. Only five technologies disrupted this trajectory of improvement, which means they brought to the market a product that was not as good as what historically had been available. Oddly, this type of technology always killed the industry leader; in none of these cases did the company that had been the leader in the prior generation survive into the next generation. Even more remarkable, these were relatively simple technologies. Let us take this phenomenon to the computer world. When we consider the sequence of minicomputers that Digital introduced into its markets through the 1970s and 1980s, it had a perfect record in developing the technologies—whether incremental or radical—that sustained the trajectory of improvement in many computers. The early personal computers that emerged in the late 1970s and early 1980s—such as the Apple II, marketed to children as a toy—were a disruptive technology. Digital received no signal from the market that the personal computer mattered because none of its customers could use personal computers. They were not good enough. Yet, because the trajectory of technological progress outstrips the ability of customers to use it, what was at one point a toy improved at such a rapid rate that it intersected with the customers’ needs of many computer users at a later point in time. A whole population of minicomputer companies was knocked out of the market together as a result of listening to their customers. When I was consulting recently with the senior management at Intel, the chair, Andy Grove, puzzled over my description of “disruptive technology,” and recast it. He said the concept could be more accurately characterized as trivial technology that disrupts the business model of the leaders, which is what makes it difficult to handle. Grove said that Digital did not have a technology problem, but rather a problem with its business model. For example, a minicomputer is fairly expensive and complex, and it has to be sold directly to the customer. Digital had to make gross margins of about 45% just to be acceptably profitable in the market. The senior management faced proposals to invest in two types of products. Some entailed developing better computers than Digital had ever made before that it could sell for $200,000 and 60% gross margins by penetrating the market where customers had historically only been able to use mainframes. Other proposals entailed investing in personal computers that could be sold for $2,000 and, in the very best of years, promised gross margins of only 40% that were headed to 20% rapidly. Grove concluded that the choice management had to make was whether to invest in better products that would serve the best customers, which would improve the company’s profit margins, or invest in worse products that their customers could not use and that would erode the company’s profit margin. This is the innovator’s dilemma. For 111 of the 116 cases in the disk drive study, these paradigms of good management— listening to your best customers and focusing investments on those innovations that promise the highest profit margins—provided good guidance for the innovators. However, in the five cases in which the disruptive technology came in, those same paradigms of good management paralyzed the leading companies and made it impossible for them to respond. From Steel Mini-Mills to Sony Let us look now at a very different industry, which is the steel industry. The question is how did the steel mini-mills in North America grow to account for half of steel production? Most of the world’s steel is made in large integrated mills that require billions of dollars to build. Mini-mills, XXII in contrast, melt scrap in electric-arc furnaces and can make steel of any given quality for a 20%lower cost than integrated mills. While it seems that every leading steel company worldwide would take on mini-mill technology because the technology is straightforward and the chance to reduce the costs of making a commodity like steel by 20% is a sure path to profit. Right? But not a single integrated steel company in North America or Europe has yet successfully invested in a mini-mill. Only recently, a few companies in Japan have acquired already successful mini-mills. When mini-mills became technologically viable in the mid-1960s, the quality they could produce was very low. Only the concrete reinforcement-bar market accepted their product because rebar had pretty loose specifications. As the mini-mills attacked the competitive rebar tier of the market, the integrated mills happily dropped out of that tier because their gross margins in that market segment were only about 7%. As the mini-mills expanded their capacity, the integrated mills shut the lines down or reconfigured them to make more profitable products. By about 1975, the mini-mills had driven the integrated mills out of the rebar market. The mini-mills, with a 20% cost advantage, made lots of money making rebar in competition with the high-cost integrated mills. But when they finally succeeded in driving the last integrated mill out of the rebar market in about 1975, the price of rebar collapsed by 20%—because you now had low-cost mini-mills slugging it out with low-cost mini-mills in a commodity market. How could they begin making money again? They had no option but to turn to products that were larger and of higher quality, which means they attacked the next tier up of the market: angle iron and thicker bar and rod. The mini-mills little by little figured out how to make better products. As they hit the next tier of the market, the integrated mills were happy to get out of it, too, because the 12% margins were still relatively low. As the mini-mills expanded capacity, the integrated mills shut the lines down and reconfigured them to make better products, and while the mini-mills were competing against the high-cost integrated players, the mini-mills once again made a lot of money—until 1984, when they succeeded in driving the last high-cost integrated player out of the angle-iron market. The price of angle iron then dropped by 20%. The mini-mills then moved up into structural beams. The margin that the integrated mills were making in structural beams was about 18%, and the market was three times larger than those the mini-mills had already conquered. In the early 1980s, beams could not be rolled in a mini-mill format to meet specifications. The mini-mills, however, figured out how to roll high-end structural bar—like 12-, 16-, and 24-inch I-beams and H-beams. By 1992, they had driven U.S. Steel out of the structural-beam market. By 1996, Bethlehem Steel had also been driven out of that market. Integrated steel companies apparently practiced good management. Every time they lopped off the low end of their product line, their reported gross-profit margins improved. Also, every time the mini-mills added the very same products to the high end of their product lines, their reported gross-profit lines improved. As a perfect symmetry of motivation, the high-end players were motivated to leave the very markets that the low-end players were motivated to enter. Other companies that recently experienced this kind of phenomenon include Sony, which came into the low end of the market with low-quality transistor pocket radios in the mid-1960s. Sony then became the highest-quality electronics maker worldwide. Seiko started with the inferior plastic digital watch and then became the highest-quality watchmaker worldwide. In the photocopier industry, Canon competed against the huge machines by Xerox with a low-end, limited-feature, tabletop photocopier that filled a niche for small companies. Xerox’s customers XXIII could not use the little tabletop machines, but in a different application, the inferior machine moved up-market, and so customers consumed infinitely more photo-copying as a result of that industry having been disrupted. Interdependent and Modular Architectures In the early 1980s, IBM had better operating- system technology than did Microsoft and better microprocessor technology than did Intel. Yet, IBM chose to outsource the two technologies to those respective companies and in the process put into business the two companies that subsequently dominated the computer industry. IBM designed and assembled computers, where subsequently no money was made. At the time IBM made those decisions, it was generally regarded as managerially astute. This experience brings up the question as to when to work inhouse and when to outsource. A review of the history of most industries reveals that during the early period when the performance of the product or service is not good enough for what customers in the mainstream need, the architecture of the product tends to be proprietary and interdependent in character. When the product is not good enough, competition is dictated through the development of better products. A proprietary architecture in an interdependent architecture can come closest to the frontier of what is technologically possible. For example, in the early years of the mainframe computer industry, an independent supplier of operating systems, core memory, or logic circuitry could not have existed because the design of XXIV each of those subsystems depended upon the design of each of the other subsystems. They had to be interdependently architectured. An independent-contract manufacturer of mainframe computers could not exist because the way mainframe computers were made depended upon the way that they were designed, and the way that they were designed depended upon the way they were going to be made. Integrated companies initially tend to dominate their industries, such as IBM and Digital, General Motors and Ford, Alcoa and U.S. Steel, and so on. In the most demanding tiers of these markets, the architectures are still proprietary and interdependent. Once the technology is more than good enough, how do companies compete for the business of customers in the now-overserved tiers of the market? The answer is that they must compete differently. They must compete in speed-to-market, in the ability to respond quickly to changes in customers’ needs, and in the ability to customize the features and functions of products to the needs of smaller and smaller niches of the market. To be fast, flexible, and responsive, the architecture of the product has to evolve from an interdependent to a modular architecture— ultimately one that is built around industry standards. When that happens, the industry tends to disintegrate as specialized companies provide one piece of value added. The population of specialized companies then tends to replace what were the dominant integrated companies in an earlier era. In fact, the dominant integrated companies have to disintegrate in order to compete effectively (see Figure 2). In an interdependent architecture, the companies that make the money tend to be the ones that do the design and assembly of the product that is not good enough, that is, the end-use product. Companies that were the suppliers tended to live a miserable profit-free existence year after year. So, for example, IBM, with 70% market share, made 95% of the industry’s profit. The companies that supplied IBM were wrung out every quarter. General Motors had a 55% market share; it made 80% of the industry’s profit. A supplier to General Motors made no money. In a modular architecture, the company that makes the money tends to flip; those that design and assemble the products that the customers use tend to get knocked out and the ones that make money are the ones who supply the subsystems that are not yet good enough. To illustrate, if an engineer at Compaq receives instructions to design a better computer than Dell, the engineer could put in a faster microprocessor, a higher-capacity disk drive, or more dynamic randomaccess memory. However, anything the engineer does, the competitor can instantly copy. So the ability to make money flips back to Intel, who provides the performance-generating sub-system that the assembler has to use in order to keep it at their leading edge. I recently published an article in Harvard Business Review called “Skate to Where the Money Will Be.” The title refers to what made Wayne Gretzky a great hockey player: He skated not to where the puck was, but to where it would be. It suggests that the place in the value-added chain where the money is made at one point is not likely where it will be made in the future. This is happening now in the car industry. Automobiles have become more than good enough for what most consumers need. The industry used to take six years to design and deliver a new car. Now the design cycle has converged on two years, and customers can order a car custom-assembled to their specifications, deliverable in five days. Car companies accomplish this by shifting the architecture of these cars from an interdependent to a modular architecture. They still pro-cure subsystems from tier 1 suppliers. Inside the subsystems, just like an Intel chip set, the architecture becomes more proprietary and interdependent even while the external interfaces of these sub-systems become more standardized. True to form, the integrated car companies are XXV having to disintegrate to keep pace with the accelerating cycles. However, car companies like GM sold off the pieces of their business where the money was subsequently likely to be made, as did IBM. In other words, GM and IBM skated to where the money used to be rather than to where the money would be in the future. Modularity in Action: Advanced Materials In many ways, the purpose of advanced materials is to be a sustaining technology; that is, to improve the functionality of products at the leading edge. When we started our company, Ceramics Process Systems, in the early 1980s, we introduced components made of ceramics to the automobile-engine world. One of the leading European car companies that was a major investor in our company wanted us to start making silicon nitride piston pins because the calculations revealed that if we could reduce the mass of a reciprocating component in the engine, it would greatly improve its efficiency. With the specifications they gave us, we molded the piston pins. When the piston pins were tested, however, the test engine vibrated uncontrollably. It turned out that over the years, the car company had distributed mass elsewhere in the engine to compensate for the reciprocating mass of the steel. There simply was not a plugcompatible modular opportunity for the advanced materials at the edge of performance. Everything depended upon everything else. We succeeded because we finally found applications where the technology was almost plug-compatible, which is far away from the leading edge. How Disruptive Growth Begins The way disruptive technology makes it to the obvious existing market is by finding simple applications and then gradually improving. Figure 3 shows that the transistor was a disruptive technology relative to the vacuum tube because it could not handle the power in the early 1950s that would be required to be used in the market as it existed at the time. Every one of the XXVI vacuum-tube players saw the transistor coming. They all worked on the technology in their laboratories, but framed it as a technological deficiency instead of an opportunity. In other words, companies were challenged with ways of making transistors good enough to be used in the vacuum-tube market. But transistors took root in a completely new market. The first application was for a small hearing aid in 1953. This application valued the transistor for the very attributes that made it useless in the mainstream market. In 1955, Sony introduced its pocket transistor radio, which was such a low-quality product that it did not compete in the mainstream market. It only appealed to low-end customers, such as teenagers, because it enabled them to do something that had not been possible before—such as listen to Elvis Presley out of earshot of their parents. Sony moved up into portable televisions in about 1959, where a huge new market emerged. Other companies felt no pain because the market served different kinds of customers and different kinds of applications than their mainstream ones. By about the mid1960s, solid-state electronic components became good enough for the mainstream market to use and they replaced vacuum tubes. This is a typical pattern. A disruptive technology first takes root away from the core of the mainstream market, where users value it despite its limitations. In the last chapter of The Innovator’s Dilemma, I discuss whether the electric vehicle and photovoltaics are disruptive technologies. In its concern over air pollution, California passed legislation in the early 1990s mandating that every car company had to sell 2% of its unit volume in California as zero-emission or electric vehicles by 1998, or it would be prohibited from selling gas-powered cars. The car companies worldwide mounted huge efforts to develop battery technology for electric vehicles. By about 1996, it was clear that they would not accomplish this goal. As an example, customers told Chrysler that they wanted a car that went about 250 miles between refueling stops and could accelerate from 0 to 60 miles per hour in about nine seconds. To get its electric minivan to accelerate fast and cruise far, Chrysler loaded 1600 pounds of leadacid batteries in the back of it. The minivan, however, only cruised 80 miles and accelerated from 0 to 60 mph in 19 seconds. One unfortunate side effect was that it took four times longer to stop this minivan than the gas-powered one because of the balance in the back. It retailed for $100,000. During consumer tests, Chrysler found no buyer. The government has since pushed the target date to 2003. In studying this issue, one of my students determined that the industry is coming up with the right answers to the wrong questions. The right question is locating the market in which a customer wants a car that does not cruise far or accelerate quickly, and is cheap. He suggested that parents of teenagers and people in the retirement community would prefer this type of car. He suggested that people in places like Bangkok would find a use for such a car since they cannot travel quickly on the streets and would actually prefer the car to shut down as they waited in traffic. Another limitation to forcing electric vehicles into existing applications is that they do not fit with existing infrastructures. If plugged into a 100-V outlet, they take an unacceptable eight hours to recharge. Even if every filling station was outfitted with 480 V of service, the car would take 20 minutes to refuel; consumers will not want to wait that long. On the other hand, if the electric vehicle were a neighborhood vehicle, designed not to drive on a freeway, but for teenagers to cruise around town to high school and see their friends, or for retirement communities, it would be convenient for the users to plug in the vehicle overnight. By targeting such a market, the car companies avoid the infrastructural interdependencies that happen when they stretch to use the new technology in the most demanding applications. Over and over again, though, leading companies try to force the technology into demanding, obvious, and large applications. XXVII One of the most personally rewarding things about The Innovator’s Dilemma has been the number of people who have told me that our theory has helped them frame a problem that they are facing in their own lives. I hope that you too will be able to use our frameworks to better understand some of the issues that your company may be confronting. Recommended Reading 1. C.M. Christensen, The Innovator’s Dilemma: When New Technologies Cause Great Firms to Fail (Harvard Business School Press, Boston, 1997). 2. C.M. Christensen, M. Raynor, and M. Verlinden, “Skate to Where the Money Will Be,” Harvard Business Review (November 2001), p. 72. 3. C.M. Christensen, T. Craig, and S. Hart, “The Great Disruption,” Foreign Affairs 80 (2) (March/April 2001), p. 80. 4. C.M. Christensen and M. Overdorf, “Meeting the Challenge of Disruptive Change,” Harvard Business Review 78 (2) (March–April 2000), p. 66. Clayton M. Christensen, the Robert and Jane Cizik Professor of Business Administration at the Harvard Business School (HBS), is the author of The Innovator’s Dilemma: When New Technologies Cause Great Firms to Fail, a book that won the Global Business Book Award for the best business book published in 1997. In 1984, Christensen co-founded Ceramic Process Systems, a developer of ceramic products, for which he served as chair and president. Christensen holds a BA degree in economics from Brigham Young University and an MPhil degree in economics from Oxford University, where he studied as a Rhodes Scholar. He received his MBA degree from HBS in 1979, graduating as a George F. Baker Scholar, and was awarded his DBA degree from HBS in 1992. Christensen was a White House Fellow, serving the secretaries of transportation. XXVIII Sobre El Sentido Del Progreso En La Teoria De Estabilidad Elastica Luis A. Godoy, Universidad Nacional de Cordoba, Argentina RESUMEN En este trabajo se propone un acercamiento epistemologico a la teoría de estabilidad elástica, considerando el pasaje de la teoría clásica a la teoría de estabilidad poscritica inicial. Se caracteriza la teoría clásica mediante el estado del arte presentado por Timoshenko en 1936, y la crisis conceptual que surge alrededor de la incompatibilidad entre resultados teóricos y experimentales para el cilindro con carga axial. Se revisan los estudios de la etapa de transición (1934- 1968) que ofrecieron una variedad de explicaciones incompletas o inadecuadas. Se presenta el surgimiento de la nueva teoría propuesta por Koiter en su tesis doctoral. A continuación se consideran dos posturas epistemologías para interpretar el cambio de teoría: la primera, debida a Kuhn, considera las teorías como paradigmas y el cambio como revolucionario; mientras que la segunda, debida a Lakatos, considera la estructura de programas de investigación. Finalmente se analizan las limitaciones y aciertos de cada una de esas visiones a la luz del cambio en la teoría de estabilidad. INTRODUCCION A partir de la década del 60 varios filósofos de la ciencia han estudiado las teorías científicas como estructuras y se han interesado en cómo se produce el cambio teórico en la ciencia. Entre las posturas mas reconocidas se encuentra la de Thomas S. Kuhn (1922-1996), centrada en el concepto de paradigma y de cambio revolucionario (Kuhn, 1962); la de Imre Lakatos (19221974) sobre programas de investigación científica (Lakatos, 1978), y la de Larry Laudan sobre tradiciones y utilidad como forma de explicar el cambio (Laudan, 1977). Alrededor de esta problemática se mueve la racionalidad o irracionalidad que tienen los científicos para aceptar un cambio de teoría y cómo es la estructura del cambio que se produce entre una teoría y otra que le sucede. ¿En qué medida esos modelos de cambio son adecuados para todas las disciplinas y todas las épocas? Según Kuhn, se trata de patrones universales, aunque los casos que sirvieron de estudio a Kuhn fueron tomados de la física y la astronomía en el pasaje de la Edad Media al Renacimiento o en los siglos XVII y XVIII. Han habido fuertes cuestionamientos a la interpretación de Kuhn, por ejemplo desde la biología (Mayr 1995). Como Mayr señala, los filósofos de la ciencia ponen demasiado énfasis en descubrimientos en desmedro de cambios en los conceptos. Sin embargo, la formación de ingenieros durante su etapa de estudios doctorales se basa en el aprendizaje de los aportes mencionados de la filosofía de la ciencia, y se pretende que el aprendiz extraiga sus propias conclusiones sobre su campo de interés. Allí es donde se nota la falta de estudios específicos que se refieran a teorías construidas en las ciencias de la ingeniería. La motivación de este estudio ha sido proveer un estudio de caso sobre el cambio teórico dentro de la mecánica aplicada, en particular referido a la teoría de estabilidad de sólidos elásticos. La historia de la teoría de estabilidad en el siglo XX representa una situación interesante sobre la contraposición entre buscar una “cosa” (la carga crítica de pandeo) versus la búsqueda de un “proceso” (el pasaje de estados críticos a poscríticos). En este trabajo revisaremos primero la XXIX teoría clásica de estabilidad estructural y como se produce una crisis conceptual. Describiremos el período de transición, en el que se buscaron diversas explicaciones a las discrepancias entre teoría y experimentos, y la nueva teoría basada en la estabilidad poscrítica inicial. Se verá el proceso de cambio desde la óptica de dos posturas de la epistemología: la de paradigmas de Kuhn y la de programas de investigación de Lakatos. El iniciador de la nueva teoría de estabilidad fue Koiter, quien visitó Brasil en dos oportunidades, en 1983, para dictar un curso de teoría de cáscaras en el LNCC/CNPq, y en 1985, cuando participó en una reunión de IUTAM y dictó un curso de estabilidad. LA TEORIA CLASICA Las características de la teoría clásica Denominaremos teoría clásica de estabilidad estructural a la vigente en la primera mitad del Siglo XX, en la cual se cuantificaba una carga de pandeo (o carga crítica, que es un valor escalar) para evaluar la inestabilidad de una estructura. A los efectos de llevar a cabo el análisis, la respuesta se computaba a partir de la configuración descargada y hasta llegar a la carga crítica, que constituía un límite de estabilidad. Era necesario imponer un modo de deformación adicional (un autovector) para generar la condición de equilibrio en un estado de equilibrio adyacente. Matemáticamente, la evaluación de la carga crítica generaba un problema de autovalores para autovectores supuestos en base a consideraciones físicas. Un buen estado del arte de la teoría clásica fue escrito por Timoshenko (1936), más adelante actualizado como Timoshenko y Gere (1961). El éxito de esta teoría estuvo centrado alrededor de la modelación de un caso inicial: la columna bajo carga axial, para la cual se verificaba experimentalmente que el procedimiento funcionaba. Debe recordarse que las estructuras prácticas que se construían en esa época (hasta inicios del siglo XX) se hacían mayormente con estructuras de barras. Este procedimiento teórico pudo extenderse usando la misma metodología a otras formas estructurales, incluyendo placas. La metodología de análisis podía llevarse a cabo por dos vías: en la formulación diferencial se debe “… suponer que la placa sufre un ligero pandeo bajo la acción de fuerzas aplicadas en su plano medio, y calcular luego las intensidades que precisan esas fuerzas para mantener la placa en esa ligera forma de pandeo. La ecuación diferencial de la superficie elástica se obtiene en ese caso … suponiendo que allí no hay carga lateral.” (Timoshenko, 1936, pp. 353). Otra vía es usando un método energético, en el cual “… suponemos que la placa, sometida a tensiones por fuerzas que se ejercen en el plano medio, experimenta alguna pequeña flexión lateral compatible con las condiciones de contorno dadas. Esta débil flexión puede originarse sin extensión de ese plano medio y solamente necesitamos considerar la energía de flexión y el trabajo correspondiente efectuado por las fuerzas que actúan en la nombrada superficie media. Si el trabajo realizado por estas fuerzas es menor que el trabajo de deformación por flexión, para cada XXX forma posible de pandeo lateral, la forma plana de equilibrio de la placa es estable. Si el mismo trabajo llega a ser mayor que la energía de flexión para cualquier forma de deformación lateral, la placa queda en situación inestable y acontece el pandeo” (Timoshenko, 1936, pp. 354). Adicionalmente, la metodología se podía también llevar a cáscaras delgadas, para las cuales no existía aún un campo de aplicación fértil, pero que era de interés mayormente teórico. Por ejemplo, R. Zoelly estudió en su tesis doctoral de 1915 el problema de esferas de pared delgada dentro del marco de la teoría clásica, llegando a expresiones sencillas que podían calcularse a mano para modos simétricos. Timoshenko no encontró objeciones a esa formulación en 1936: “Hasta ahora hemos considerado únicamente el pandeo simétrico de la lamina pero un estudio mas general prueba que debido a la simétrica de la lamina esférica comprimida uniformemente, respecto de cualquier diámetro, la ecuación … deducida de la hipótesis de simetría … puede utilizarse siempre en el cálculo de la tensión crítica.” (Timoshenko, 1936, pp. 535). También se lograron expresiones para el cilindro con carga axial y para el cilindro con presión lateral. La gran ventaja de la formulación clásica estaba asociada a su simplicidad, compatible con los escasos recursos de cálculo disponibles en esa época. Podría pensarse que el progreso de los recursos de cálculo se tradujeron en el progreso teórico en este campo. Sin embargo, notaremos que no fue el ingreso de la computadora sino el cambio conceptual el que posibilitó la gestación de un nuevo enfoque a la problemática. La evidencia experimental adversa a la teoría clásica ¿Porqué el enfoque clásico comenzó a mirarse críticamente? El viraje de apreciación estuvo claramente asociado a la evidencia contraria que se encontró para un caso considerado importante en su época: el cilindro bajo carga axial. Si se calculaba la carga critica siguiendo el procedimiento clasico, para un modo de pandeo con m semiondas en direccion axial y n ondas en direccion circunferencial (representativo de borde simplemente apoyado) se obtenia una formula muy simple para la tension critica σcr , dada por σcr = E h /{√[3(1-v)]} donde a es el radio del cilindro y h el espesor, E el modulo de elasticidad y v el coeficiente de Poison. El conflicto surgio porque estos σcr son valores mas altos que los que se median en experimentos de laboratorio sobre modelos en escala reducida, para cilindros de duraluminio, de acero y de bronce: “En todos los casos, la falla ocurrió a una tensión mucho menor que la que predice la teoría. En ningún caso la tensión ultima fue más del 60 % de la teórica” (Timoshenko, 1936, pp. 497-498). La Figura 243 de Timoshenko (1932) muestra en abscisas la relación entre la carga teórica clásica calculada y la obtenida en experimentos. En realidad, en muchos casos se obtenían valores del orden del 15 al 30% del valor que predecía la teoría clásica. XXXI “Se observa claramente que la razón de la tensión de ruptura a la teórica decrece cuando la razón a/h aumenta, es decir que la discrepancia entre el experimento y la teoría es mayor en las láminas más delgadas” (Timoshenko, 1936, pp. 498). Este estado de conocimientos generó una gran desconfianza hacia la teoría clásica como forma de evaluar una carga crítica. A pesar de que el caso disparador de la crisis fue el cilindro con carga axial, sin embargo la esfera bajo presión uniforme ofrecía aun mayores dificultades. Siguiendo la teoría clásica, la carga critica de la esfera era aun mas inadecuada que la del cilindro, pero esto no resulto evidente sino hasta tiempo después. Las razones asociadas a que la esfera no fuera tomada como un caso critico pueden ser dos: (i) no habían experimentos confiables sobre esferas, mucho mas complicados que los del cilindro; y (ii) no había urgencias planteadas desde la industria aeronáutica para evaluar inestabilidad de esferas. Otra de las deficiencias de la teoría clásica fue la falta de información sobre la trayectoria poscrítica: “La profesión de ingeniería estuvo satisfecha por mucho tiempo con el conocimiento del límite de estabilidad… Se tomó la posición que, por seguridad, la carga en una estructura debe siempre mantenerse por debajo de ese limite, haciendo que fuera superfluo investigar que puede ocurrir por encima de ese límite” (Koiter, 1945, pp. 3). Esta situación cambió con la necesidad de un mejor aprovechamiento estructural del material: “En la tecnología moderna, más específicamente en el diseño de aviones en los que la economía de peso es de gran importancia, esta excedencia de carga límite está ciertamente permitida!” (Koiter, 1945, pp. 4). De modo que existía la necesidad de evaluar el comportamiento poscrítico para aprovechar mejor la capacidad portante de placas, y sin embargo no se contaban con maneras confiables de computarla. Nótese que de estos tres problemas señalados (cilindro, esfera y placa) sólo el primero produjo una crisis en la teoría clásica como para ponerla en jaque. El rechazo a la teoría y el retorno a la experimentación Como respuesta operativa ante la falta de acuerdo en cilindro con carga axial, se llevaron a cabo gran cantidad de experimentos de laboratorio con diferentes niveles de cuidado. Los pioneros fueron Robertson en 1928, Lundqvist en 1933 y Donnell en 1934, entre otros. Se observó gran dispersión de los resultados de las cargas máximas que podía alcanzar una cáscara cilíndrica, pero se observaba una clara tendencia a mayores diferencias entre teoría y cálculo para valores grandes de la relación a/h (radio/espesor de la cáscara). Los estudios “… mostraron también que las investigaciones teóricas desarrolladas para una cáscara cilíndrica ideal pueden ser usadas sólo como una guía para desarrollar formulas empíricas basadas en numerosos experimentos” (Timoshenko y Gere, 1961, pp. 473). XXXII Esa desconfianza se extendió a todo modelo teórico en este campo, y la forma de cálculo pasó a basarse en formulas empíricas obtenidas a partir de los experimentos disponibles. En lugar de comprender más el fenómeno, los ingenieros se dedicaron a describirlo en más detalle dentro de los rangos de interés industrial. LA TRANSICION: CUESTIONAMIENTOS Y EXPLICACIONES EN EL MARCO DE LA TEORIA CLASICA Aproximadamente entre 1934 y 1968 hubo intentos de explicar las razones de la discrepancia entre la teoría clásica y los experimentos. Timoshenko, en la primera edición de su libro, reporta la siguiente explicación, que le parece satisfactoria: “Para explicar este desacuerdo, L. H. Donnell anticipó una teoría que tiene en cuenta los desplazamientos iniciales de la superficie cilíndrica ideal y analizó la flexión de la lamina debida a esta imperfección inicial, suponiendo que las flechas no son pequeñas. Admitió también que falla cuando comienza la fluencia del material. Tomando los desplazamientos iniciales en forma de ondas e igual longitud en las direcciones axial y circular, combinadas con ondas de pandeo simétrico con respecto del eje, Donnell encontró que la carga de falla … se puede expresar en función de la razón radio espesor a/h… Se advierte que existe un acuerdo satisfactorio entre estas curvas y los resultados de los ensayos” (Timoshenko, 1936, pp. 498-499). En la segunda edición de su libro, Timoshenko ya no es tan optimista con respecto a la explicación anterior e incluye más explicaciones alternativas: “Una investigación adicional para las discrepancias entre teoría y experimentos fue realizada [por von Karman y Tsien, 1941] estudiando el comportamiento postcrítico de cáscaras cilíndricas ideales en compresión… Suponiendo pandeo y tomando una expresión para [el desplazamiento] w con varios parámetros… Vemos que para originar pandeo en un caso ideal debemos tener una tensión de compresión dada por la ecuación [clásica], pero con un aumento de la deflexion la carga requerida para mantener la cáscara cilíndrica en la condición pandeada rápidamente disminuye y se acerca a cerca de un tercio de la carga de pandeo requerida teóricamente” … “Por eso la flexión comienza cuando la carga es pequeña y las deflexiones alcanzan los valores a los cuales la continuación del pandeo requiere de una carga mucho menor que la teórica para el caso ideal” (Timoshenko y Gere, 1961, pp. 472-473). Hay también otra explicación disponible de 1950: “En un siguiente estudio [Donnell y Wang, 1950] de la influencia de imperfecciones en el proceso de pandeo se supuso que la cáscara cilíndrica tiene inicialmente ondas … Se ve que la imperfección más pequeña reduce considerablemente la carga máxima que puede tomar la cáscara cilíndrica en compresión” (Timoshenko y Gere, 1961, pp. 473). Esos intentos trataban de corregir o mejorar la formulación analítica clásica. En resumen, podemos señalar las siguientes explicaciones sobre la discrepancia, la mayoría de las cuales fueron consideradas por Donnell (1976) y Esslinger y Geier (1975): XXXIII (a) La teoría clásica de laminas empleada en los modelos no era lo suficientemente exacta. Sin embargo, se puede demostrar que la influencia de los términos despreciados en la formulación es pequeña comparada con las grandes discrepancias presentes entre experimentos y teoría, de manera que esa explicación debió desecharse. (b) No se había considerado la trayectoria poscrítica del cilindro, que cae después del estado crítico. Esta explicación de B. Almroth (1963) llevó a evaluar la trayectoria poscrítica e intentar identificar su punto más bajo como valor de carga de pandeo. En principio se consideraba el modo crítico y se investigaba la trayectoria poscrítica con deformaciones en ese modo. “La sensación de satisfacción en el progreso hacia un límite inferior de cargas poscríticas llegó a un final abrupto cuando Hoff [Hoff, Madsen, y Mayers, 1966] … realizó la observación que parece que esos cálculos basados en muchos términos de series darán en definitiva una carga poscrítica nula” (Esslinger y Geier, 1975, pp. 110). Eso contradecía la evidencia que la carga critica no era nula, de modo que esto hizo abandonar esa explicación. (c) Se habían tratado los números de ondas del modo de pandeo supuesto como variables continuas en lugar de considerárselas como variables enteras. Las investigaciones basadas en números enteros de ondas (Hoff, Madsen, y Mayers, 1966) mostraban que sobre la trayectoria poscrítica las cargas no llegaban a cero, y los valores mínimos tenían una cierta concordancia con los experimentos; “… sin embargo, la teoría producía un número de curvas y no había criterio para seleccionar la curva que aparecería en el cilindro real para un largo determinado” (Esslinger y Geier, 1975, pp. 112). (d) Las condiciones de contorno analíticas no se satisfacían en los experimentos y viceversa. Este explicación fue sostenida por J. Singer durante algún tiempo, pero fue abandonada cuando surgió la teoría de Koiter con fuerza en la década del 70. “Despreciar la influencia de los bordes… está bien justificada por los propios ensayos, en los cuales no ocurre una dependencia del fenómeno de pandeo con el algo del cilindro o con las condiciones de borde. Sin embargo, esto también es aceptable en forma teórica” (Koiter, 1945, pp. 185). (e) No se había considerado la posibilidad de que haya un salto de un estado de equilibrio a otro entre una posición precrítica y una poscrítica. Esta explicación se debe a T. von Karman y H. S. Tsien (1941). “Debido a que los desplazamientos supuestos por von Karman y Tsien no pueden reproducir la solución general en la carga critica, sus resultados para cargas que no se desvíen excesivamente de la carga de pandeo presumiblemente no son tan buenos” (Koiter, 1945, pp. 177). (f) No se habían considerado imperfecciones en la respuesta, que pueden ser la causa de una caída en la carga teórica de pandeo. El principal estudioso de esta explicación fue Donnell, como vimos antes. XXXIV La teoría clásica coexistió con estas explicaciones durante algún tiempo, y se generaron expectativas de solucionar las dificultades de la teoría clásica mediante extensiones. Las evidencias en contra de las explicaciones (a-e) ofrecidas por diversos autores demostraron que no se podían sostener; sin embargo continuaron vigentes por algún tiempo hasta que finalmente se desvanecieron en la literatura. ¿Porqué se aceptaron esas explicaciones inadecuadas en su momento? Donnell afirma que se aceptaban por su conveniencia: “Esas explicaciones traían beneficios porque les daban a los diseñadores valores aceptables con el respaldo de una explicación teórica, especialmente (d-e), a pesar de que: (i) los valores encontrados mediante el uso de esas explicaciones no se correspondían con los factores reales; (ii) no tenían una justificación real; y (iii) producían valores demasiado conservadores en algunos casos” … “Sin ese respaldo los ingenieros hubieran tenido que enfrentar la horrorosa verdad que sus construcciones tenían diversos defectos que afectaban significativamente su capacidad resistente… Pero los ingenieros deben vivir y trabajar en un mundo real…” (Donnell, 1976, pp. 394). Sin conocer la tesis de Koiter, Donnell postuló que (f) era la causa de las discrepancias entre teoría clásica y experimentos. Esta explicación “… fue cuestionada por Cox (1940) y por von Karman y Tsien (1941) quienes notaron que esas desviaciones iniciales deberían ser varias veces mayores que el espesor de la pared para explicar los valores experimentales bajos; pero esas desviaciones no podrían haber escapado a que las notaran otros investigadores … Además, Cox y von Karman y Tsien señalaron que la explicación de Flugge-Donnell requeriría la evolución gradual del pandeo al aumentar la carga, mientras que los ensayos mostraban un pandeo abrupto y casi explosivo; tampoco se podían explicar de manera satisfactoria la gran dispersión de los puntos de los ensayos” (Koiter, 1945, pp. 4). Había además una explicación extendida cualitativa que servía para tomar en cuenta los casos que fallaban en la teoría clásica y también los que lo confirmaban (la columna) (Donnell, 1976, pp. 395). Ninguno de los trabajos elaborados durante el periodo de transición producían explicaciones satisfactorias por si mismos o combinados, y por ello no lograron establecer una nueva base explicativa con un desarrollo teórico aceptable por la comunidad científica en general. Habían intentos de corregir errores individuales, pero sin reconstruir la teoría clásica. En realidad, no se trataba de aferrarse a una teoría antigua (como postula Kuhn), sino que nadie sabía como desarrollar una nueva. El papel que cumplió la transición fue fundamental: (i) sin ella no habría sido posible recombinar ideas viejas y sumarles nuevas; (ii) prepararon el campo para generar nuevos términos; (iii) descartaron posibilidades, que de otra manera hubieran permanecido latentes como explicaciones alternativas; y (iv) se estableció claramente que había un vacío en el conocimiento, a pesar del trabajo intenso de los expertos de la época. XXXV LA TEORIA DE ESTABILIDAD DE LA REGION POSCRITICA INICIAL Las características de la nueva teoría Warner T. Koiter (1914-1997) escribió su tesis doctoral en Holanda en 1945, pero recién en la década del 60 se difundieron sus trabajos en Estados Unidos y Europa. Koiter señala: “De los ejemplos anteriores es claro que las teorías de estabilidad formuladas en el pasado son insuficientes. Deben ser suplementadas de tal manera que aun el comportamiento de estructuras diferentes, que difieren en la vecindad de la carga de pandeo teórica, pueda ser descripta” (Koiter, 1945, pp. 4). Las contribuciones de Koiter constituyen una nueva teoría, desarrollada desde el inicio de manera sistemática y consistente, con bases matemáticas sólidas y aproximaciones ingenieriles que se hacen explícitas. Algunos aspectos salientes de esa teoría son los siguientes: (a) La formulación está basada en la energía potencial total del sistema estructural, en lugar de usar consideraciones de equilibrio directo. Por esa vía se rescataban la trayectoria de equilibrio precrítica y la carga crítica clásica. (b) Koiter requería de evaluar la trayectoria poscrítica en sus etapas iniciales (a diferencia de otros estudios de la etapa de transición que precisaban la totalidad de la trayectoria para trabajar). (c) Matemáticamente, la nueva teoría requiere de un desarrollo en serie de Taylor (o de un análisis de perturbaciones). También o de un análisis de autovalores y autovectores. (d) Permitió confirmar las sospechas sobre la importancia de las imperfecciones en la estabilidad del sistema. “No sólo que el valor de la carga critica esta influenciado significativamente por las desviaciones de la estructura con respecto al modelo, sino que la naturaleza del fenómeno de pandeo es completamente diferente en la estructura y en el modelo” (Koiter, 1945, pp. 92). (e) Se generó el término “sensibilidad ante imperfecciones”. (f) Demostró cómo se produce la interacción de modos acoplados en presencia de imperfecciones pequeñas en la estructura. Los éxitos de esta teoría están asociados a dos aspectos centrales: Primero, las predicciones de la nueva teoría se verificaban experimentalmente frente a experimentos realizados antes o con experimentos nuevos. J. Roorda llevó a cabo experimentos en 1964 para probar los resultados teóricos de Koiter (Roorda, 1964). En segundo lugar, la nueva teoría lograba explicar y modelar matemáticamente el comportamiento de casos difíciles (como el cilindro y la esfera) y también de casos sencillos (la columna). A pesar de que la nueva formulación era complicada, sin embargo podía usarse sin necesidad de contar con una capacidad de cómputo importante. Koiter mismo nunca usó computadoras en sus trabajos, y las extensiones para computar su teoría con XXXVI elementos finitos ha sido mucho más recientes. Tercero, es posible generalizar la teoría de manera de llevarla a diversos casos estructurales. Las ventajas de la teoría incluye el proveer curvas correctas poscríticas en las etapas iniciales, para desplazamientos menores al espesor de la cáscara, para lo cual se requiere de poco esfuerzo computacional. Además la teoría provee criterios de estabilidad de la estructura en cualquier configuración de carga, incluyendo la carga critica. Esto posibilita clasificar los posibles comportamientos de acuerdo a las trayectorias poscríticas que se generan, o de acuerdo a indicadores basados en la energía del sistema. La teoría proveyó una clasificación de los posibles comportamientos esperables en cualquier estructura. El análisis proveyó los casos de bifurcación estable, inestable, asimétrica y punto de inflexión, los cuales eran todo lo que le podía ocurrir a un sistema estructural al llegar al estado critico. Conceptos previos mantenidos en la teoría de Koiter Consideremos primero los siguientes interrogantes: ! ! ! ¿Qué quedó de la teoría clásica? En la teoría de Koiter quedaron la carga crítica (como referente y caso “ideal”, al que no se puede llegar en la práctica) y el modo crítico, que eran parte de la teoría clásica. ¿Qué cosas nuevas hay que evaluar? En la teoría clásica no era necesario evaluar la trayectoria poscrítica (inicial), su estabilidad y la sensibilidad ante imperfecciones. Todos estos elementos son cruciales en la nueva teoría. ¿Qué cosas relaciona la nueva teoría? Relaciona la estabilidad de la trayectoria inicial con la caída en la carga de pandeo con respecto a la clásica. Veamos que elementos conocía Koiter durante el desarrollo de su teoría. En primer lugar, Koiter utilizó el criterio energético para evaluar la estabilidad de un sistema. El criterio mismo no era nuevo y Koiter cita como caso antecedente a Bryan (1888): “… Su trabajo parece haber sido el primero en intentar el desarrollo de una teoría general de estabilidad. Su trabajo se basaba en el criterio energético, que postula que un estado de equilibrio es estable o inestable dependiendo de si la energía potencial en ese estado tiene o no un mínimo. Sin embargo sus cálculos de la energía elástica toma en cuenta solo términos cuadráticos en los desplazamientos. La segunda variación de esta energía entonces es de la misma forma que la propia energía y es positiva como ella… la segunda variación de la energía potencial total es también siempre positiva de modo que la inestabilidad en esos casos queda excluida” (Koiter, 1945, pp. 1). La principal fuente de la teoría fue, como Koiter mismo señala, los trabajos de Trefftz (1933) quien uso el criterio energético para evaluar la estabilidad. Pero las limitaciones de estos enfoques consisten en que al restringir la energía a contribuciones cuadráticas (en lugar de cuárticas) en función de los desplazamientos sólo era posible considerar el estado neutro de estabilidad: “Las consideraciones generales de estabilidad desarrolladas anteriormente y discutidas aquí estaban restringidas a la investigación de la estabilidad neutra y específicamente XXXVII estaban orientadas hacia la determinación del limite de estabilidad. Los fenómenos que aparecen al alcanzar o aun exceder el limite de estabilidad no eran considerados” (Koiter, 1945, pp. 3). Un segundo ingrediente tomado por Koiter fue la influencia de imperfecciones pequeñas. Pero mientras que Donnell consideraba que las imperfecciones se amplificarían al aumentar la carga hasta que el material entrara en fluencia, Koiter considero la influencia sobre un proceso de bifurcación, sin introducir plasticidad en la explicación. Un tercer elemento es el modo de pandeo, que estaba presente en la teoría clásica. Ahora ese concepto juega un papel central, y la nueva teoría admite modos aislados y también modos acoplados. En la nueva teoría el modo se puede determinar mediante un análisis de autovectores. Cuestionamientos y limitaciones de la teoría de Koiter Cuando la nueva teoría se extendió tuvo que enfrentarse a críticas de otros investigadores. Los principales cuestionamientos surgidos en la teoría fueron los siguientes: (a) El comportamiento de una cáscara en la región poscrítica inicial no es un criterio confiable para predecir su sensibilidad ante imperfecciones (Kempner, 1968). Se encontró un contraejemplo en este sentido: un cilindro elíptico bajo carga axial tiene un comportamiento que sigue la teoría de Koiter en su primer carga crítica, pero luego recupera su capacidad portante y puede ser sometido a cargas mucho mas altas. (b) No es posible predecir con exactitud la respuesta poscrítica avanzada basándose en la respuesta poscrítica inicial. Esta limitación surgió como consecuencia del empleo de tecnicas de perturbación a partir del entorno del estado crítico. El hecho de evidencia en contra (especialmente el caso de no predecir correctamente la carga de pandeo del cilindro elíptico) no hizo que la teoría fuera rechazada: “La teoría de Koiter soportó el ataque y es usada en numerosas publicaciones” (Esslinger y Geier, 1975, pp. 113). Si bien Koiter mismo sólo trabajó con sistemas continuos, su teoría fue extendida a sistemas discretos, como se reseña en (Godoy, 2000). Proporcionó un campo fértil sobre el cual se pudo seguir trabajando. Fue confirmada teóricamente por la teoría de catástrofes en los 70 y 80. ESTABILIDAD COMPUTACIONAL La teoría de Koiter ha coexistido con un desarrollo paralelo, que ha usado los términos y nivel de comprensión logrados por Koiter. El avance en capacidades de computación y el desarrollo de algoritmos para seguir problemas no lineales hizo que se desarrollara una nueva forma de trabajo, con menos énfasis en la teoría y mas énfasis en el cómputo. La estabilidad computacional (Bushnell, 1985) pone énfasis en el cómputo de las trayectorias de equilibrio usando técnicas numéricas; no usa técnicas de perturbación sino técnicas incrementales de avance, que son más eficientes. Debemos señalar que la teoría de Koiter también se puede computar mediante el método de elementos finitos, pero la precisión para el cálculo de trayectorias poscríticas es menor que en la estrategia de computar trayectorias paso a paso. XXXVIII La motivación detrás de este enfoque ha sido la necesidad de contar con programas de elementos finitos para usuarios masivos. Desde el punto de vista del usuario, hubo un cambio de énfasis en la comprensión por uno de descripción. Pero el enfoque computacional al problema de pandeo también tiene sus limitaciones: por ejemplo, los algoritmos pasan por alto los puntos críticos, les cuesta cambiar de trayectorias, no proveen información sobre la estabilidad misma de los estados de equilibrio. En todas las soluciones intentadas se vuelve a la teoría de Koiter (por ejemplo, para cambios de trayectoria se usan perturbaciones hasta encontrar un estado de equilibrio). LA VISIÓN DE PARADIGMAS Y REVOLUCIONES DE KUHN En esta sección no intentaremos describir la teoría de Kuhn sobre el cambio científico, dado que esa tarea escapa a las limitaciones de un trabajo y a las posibilidades del autor. La versión original de este enfoque se encuentra en Kuhn (1962), mientras que una versión modificada fue presentada en Kuhn (1981). En lugar de eso supondremos cierta familiaridad del lector con la teoría de Kuhn y pasaremos a ilustrar de que manera esa teoría permite interpretar la situación de la estabilidad elástica al cambiar del enfoque clásico al nuevo. La identificación de paradigmas en la teoría de estabilidad Un aspecto central en el análisis de Kuhn es el de paradigma. El concepto mismo de paradigma no es fácilmente definible, como han notado muchos filósofos de la ciencia, dado se incluyen allí los supuestos teóricos, las leyes y las técnicas para su aplicación que los miembros de una comunidad científica adoptan en un momento determinado. Kuhn explicita el papel desempeñado por un paradigma como vehículo para la teoría científica: “…su función es la de decir a los científicos que entidades contiene y no contiene la naturaleza y como se comportan esas entidades. Esta información proporciona un mapa cuyos detalles son elucidados por medio de las investigaciones científicas avanzadas… este mapa es tan esencial como la observación y la experimentación para el desarrollo continuo de la ciencia… Al aprender un paradigma, el científico adquiere al mismo tiempo teoría, métodos y normas, casi siempre en una mezcla inseparable” (Kuhn, 1962, pp. 173-174). Lo primero que nos preguntamos es si las teorías clásica y poscrítica inicial llegan a constituir paradigmas en la concepción de Kuhn. Esto también permitirá establecer si ha habido realmente un cambio de paradigma. Podemos afirmar que la teoría clásica fue el paradigma fundacional en la disciplina. Timoshenko explica el estado de situación hacia 1936: “Necesidades prácticas de carácter urgente originaron en los últimos años amplias investigaciones teóricas y experimentales acerca de las condiciones que rigen la estabilidad de los elementos comprimidos… Parece haber llegado el momento en que esos trabajos, conservados en diferentes lugares y en distintos idiomas, y que son con frecuencia de difícil acceso para los ingenieros que los precisan como normas de sus proyectos, se compilen y lleguen a formar un libro” (Timoshenko, 1936, Prologo). XXXIX El nombre dado por Timoshenko a su libro de 1936, “Teoría de estabilidad elástica”, pasó a identificar el área de trabajo y se constituyó en el referente para todos aquellos que practicaban la especialidad o eran usuarios de ella. Trabajar en esta área (o paradigma) era contribuir a llenar los vacíos dejados por el libro, evaluando nuevas cargas críticas de pandeo con la metodología establecida, tanto experimental como analítica. Esto no significa que no hubiera antes de 1936 un cuerpo de conocimientos sobre estabilidad, sino que ese era un cuerpo disperso y se constituyó en paradigma asociado a la contribución de Timoshenko. Entendemos que uno de los aspectos que pone en evidencia la identidad de un paradigma es el cambio de nombre de la teoría que lo designa. En el caso que estudiamos, la teoría clásica se llamaba “Teoría de estabilidad elástica”, mientras que la nueva teoría se identifica como “Teoría general de estabilidad elástica”. La distinción radica en una palabra (“general”); sin embargo, tiene las implicancias que la teoría clásica carecía de generalidad, se constituía por medio de una serie de casos resueltos sin una unidad de principios y sin unidad metodológica. Mas aún, ambas teorías hacen cosas distintas y buscan entidades distintas, de naturaleza diferente: una cosa (carga critica) en la teoría clásica, y un proceso (el pasaje del estado crítico al poscrítico) en la nueva teoría. Un segundo aspecto constituye la aparición de libros de texto en el proceso revolucionario de la ciencia: “… puesto que los libros de texto son vehículos pedagógicos para la perpetuación de la ciencia normal, siempre que cambien el lenguaje, la estructura de problemas o las normas de la ciencia normal, tiene, íntegramente o en parte, que volver a escribirse … Así pues, los libros de texto comienzan truncando el sentido de los científicos sobre la historia de su propia disciplina y, a continuación, proporcionan un sustituto para lo que han eliminado” (Kuhn, 1962, pp. 214). Un tercer aspecto es la redefinición de la historia que condujo al paradigma y de la galería de héroes: “Por razones que son obvias y muy funcionales, los libros de texto científicos… se refieren sólo a las partes del trabajo de científicos del pasado que pueden verse fácilmente como contribuciones al enunciado y a la solución de problemas paradigmaticos de los libros de texto. En parte por selección y en parte por distorsión, los científicos de épocas anteriores son representados implícitamente como si hubieran trabajado sobre el mismo conjunto de problemas fijos y de acuerdo con el mismo conjunto de cánones fijos que la revolución mas reciente en teoría y metodología científica haya hecho presentar como científicas” (Kuhn, 1962, pp. 215). Es interesante observar que el nombre de Henry Poincaré, quien trabajó hacia finales del siglo XIX, no aparece citado en ninguna de las ediciones de Timoshenko; sin embargo, es parte de la historia recuperada en los libros del nuevo paradigma (Thompson y Hunt, 1973), porque a él se remontan las técnicas de perturbación, necesarias en la teoría poscrítica inicial pero no en la clásica. Algo similar ocurre con Lyapunov, quien sentó las bases para comprender el concepto de estabilidad; pero ese concepto aparece como marginal en la teoría vieja y como central en la nueva. Y de Trefftz, quien desarrolló el método energético. Por lo tanto hay una redefinición de quienes son los precursores en el área de trabajo. XL Un cuarto aspecto es que la nueva teoría no está formada por correcciones a la teoría clásica; esto se había intentado en el periodo que denominamos de transición, pero sin éxitos significativos porque no se avanzó en la comprensión de los fenómenos no explicados o anomalías. La nueva teoría debe comenzar definiendo axiomas y construye conocimientos de una manera más sistemática que en la teoría vieja. Postulamos aquí que hay dos paradigmas bien establecidos, y que hubo un verdadero cambio de paradigma entre la teoría clásica y la poscrítica inicial; sin embargo, veremos que las consecuencias de ese cambio no son tal como las describe Kuhn sino que presentan otros matices. Además, el nuevo paradigma nunca adquirió el monopolio, de manera que han subsistido ambos paradigmas aunque a veces entren en conflicto. Anomalías Kuhn menciona que los descubrimientos de los que surgen nuevos tipos de fenómenos presentan algunas características: “…la percepción previa de la anomalía, la aparición gradual y simultánea del reconocimiento tanto conceptual como de observación y el cambio consiguiente de las categorías y los procedimientos del paradigma, acompañados a menudo por resistencias” (Kuhn, 1962, pp. 107). Consideremos dos anomalías vistas en las secciones anteriores. Entendemos que la teoría de Kuhn permite acomodar adecuadamente ambos casos, cuyo resultado fue diferente. Por el contrario, el concepto de anomalía no aparece explícitamente en Lakatos. (a) La anomalía del cilindro con carga axial hizo tambalear a la teoría clásica. Esta puede interpretarse en el marco siguiente: “…una anomalía sin aparente importancia fundamental puede provocar una crisis si las aplicaciones que inhibe tiene una importancia práctica particular…” (Kuhn, 1962, pp. 135-136). Vale decir, la anomalía es significativa por no permitir predecir adecuadamente la inestabilidad de un problema urgente para la industria aeronáutica. Pero hay otra característica más de esta anomalía, que pertenece al grupo de “…las anomalías reconocidas cuyo rasgo característico es su negativa tenaz a ser asimiladas en los paradigmas existentes” (Kuhn, 1962, pp. 157). En este sentido vimos como fue difícil para los investigadores de la transición poder explicar las discrepancias anómalas como parte de la teoría clásica. (b) La anomalía del cilindro elíptico bajo carga axial, por el contrario, no hizo temblar a la teoría de Koiter. ¿Que diferencia hay con la anterior anomalía? “Aparentemente, tampoco había parecido lo suficientemente importante como para provocar el malestar que acompaña las crisis; pudiendo reconocerse como ejemplos en contrario y, no obstante, ser relegados para un trabajo posterior” (Kuhn, 1962, pp. 135). XLI De manera que la anomalía del cilindro elíptico cayo en un lugar latente: se comprendía porque la teoría no lo podía tomar en cuenta, pero no se contaba con un remedio que lo permitiera incluir adecuadamente. Esa paso a ser una de las limitaciones de la nueva teoría, que se concentraba en la vecindad del estado crítico y no llegaba mas lejos, como lo hace la estabilidad computacional. El cambio de términos y conceptos entre paradigmas Kuhn acierta al decir que los términos no se aprenden separados o aislados, sino que vienen en grupo y es allí donde toman sentido. Los conceptos que existían antes de la nueva teoría incluían la carga crítica, el modo de pandeo, y en el periodo de transición habían llegado a incorporar la trayectoria poscrítica, pero eso no bastó para acomodar los cambios revolucionarios. Lo nuevo (Koiter) no se puede describir completamente en términos de lo viejo (teoría clásica). Antes no había conceptos construidos para estabilidad poscrítica inicial, ni para sensibilidad ante imperfecciones. Por ejemplo, Donnell había introducido en esta área de la ciencia el término de imperfección, pero no con el enfoque de Koiter, que le dio un viraje nuevo. Por lo tanto, hay un vocabulario nuevo, términos nuevos y conceptos nuevos. Eso no excluye que esos nuevos términos no hayan sido aprendidos por los investigadores que continuaron trabajando en la teoría clásica. El concepto de modo en la teoría clásica era una forma única e interesaba sólo como paso intermedio para llegar a la carga crítica. En la versión de Donnell se hablaba del modo postcrítico, pero también como forma inmutable. Mucho después se introduce la idea que el modo postcrítico puede evolucionar a medida que avanza el proceso de deformación. Koiter recupera tanto el modo único como el acoplado, no como forma de evaluar la trayectoria poscrítica avanzada sino sólo como manera de tomar una dirección de deformación hacia la cual la estructura tendería al inicio de los estados poscríticos. Si bien previamente ya había conceptos de estabilidad debidos a Lyapunov, Koiter incluyó la estabilidad en el sentido de Trefftz, como término predictivo que forma parte del análisis. Entonces la estabilidad deja de ser una cualidad teórica secundaria y pasa a ser un elemento útil para la clasificación. La clasificación del comportamiento no era posible (ni se vislumbraba) antes de Koiter. La nueva teoría toma un carácter holista al clasificar los tipos de comportamiento posibles. Como tal, da una estructura a la teoría. En la nueva teoría, algunos términos, como modo de pandeo y estabilidad, se conectan con la física del problema de una manera distinta. Y esto altera el conjunto de situaciones con las que se relacionan estos conceptos. Los problemas de traducción se ven facilitados enormemente por la transición, que incorpora términos necesarios para el nuevo enfoque, como los de trayectoria poscrítica e imperfecciones. Quizás términos como carga crítica ya no son idénticos, pierden el carácter predictivo que tenían en la teoría clásica y ahora adquieren un carácter de referencia, pasan a ser un valor en el cual apoyarse y son útiles para buscar un nuevo término que si tenga carácter predictivo. Ese nuevo término es la carga máxima (evaluada en la trayectoria imperfecta no lineal) que sólo adquiere sentido en conjunto con imperfecciones, respuesta inicial y estabilidad del estado crítico. XLII ¿Hay revolución en el sentido de Kuhn? El concepto de revolución de Kuhn ha sido duramente criticado desde la óptica de la biología. Según Mayr (1995), en biología no hay revoluciones en el sentido de Kuhn. Por ejemplo, en la clasificación sistemática no hubo una sustitución revolucionaria porque los dos paradigmas se siguieron usando. Mayr señala: “No hubo una revolución en la que se rechazara la ciencia anterior. No hubo paradigmas inconmensurables” (Mayr, 1995, pp. 115). En la teoría de estabilidad aún hoy los programas de computadora para propósitos generales que usan elementos finitos, pueden calcular tanto las cargas críticas (teoría clásica) como las trayectorias no lineales (teoría poscrítica). Es del conjunto de enfoques que el ingeniero interpreta la realidad o toma decisiones, y asigna a cada elemento de juicio un peso para interpretar su objeto de estudio. En la teoría de estabilidad es claro que hubo una revolución, pero no un cambio repentino como dice Kuhn, ni tampoco irracional y excluyente. El conflicto entre paradigmas ciertamente existe en la teoría de estabilidad “Así pues, es evidente que debe haber un conflicto entre el paradigma que descubre una anomalía y el que, más tarde, hace que la anomalía resulte normal dentro de las nuevas reglas” (Kuhn, 1962, pp. 156). Pero eso no hace que ambos paradigmas resulten mutuamente excluyentes, como pretende Kuhn por ejemplo en este párrafo: “Por consiguiente, demos ahora por sentado que las diferencias entre paradigmas sucesivos son necesarias e irreconciliables” (Kuhn, 1962, pp. 165). Tampoco es cierta la imagen de revoluciones cortas y bien definidas con largos periodos intermedios de ciencia normal. La teoría clásica de estabilidad se consolidó como paradigma alrededor de 1936, pero casi coincidentemente se inició el periodo de transición en la búsqueda de solución de la anomalía del cilindro, que duró alrededor de 30 años. Nunca hubo cambio irracional del punto de vista de los científicos, basados en cuestiones de valores, sino que los científicos lograron ver el campo formado por dos paradigmas que coexisten aún. Siempre fue posible comparar los paradigmas entre ellos, y no han sido imposibles la traducción y la interpretación. Nos queda siempre, por cierto, la alternativa de sólo llamar revoluciones en la terminología de Kuhn, a aquellas que cumplan con los requisitos que él señala, incluyendo (i) que “los proponentes de paradigmas que están en competencia estarán a menudo en desacuerdo con respecto a la lista de problemas que cualquier candidato a paradigma deba resolver”; (ii) que “en el nuevo paradigma, los términos, los conceptos y los experimentos antiguos entran en relaciones diferentes unos con otros”; y (iii) que “quienes proponen los paradigmas en competencia practican sus profesiones en mundos diferentes… ven cosas diferentes y las ven en relaciones distintas unas con otras” (Kuhn, 1962, pp. 230-233). Pero esta alternativa no parece estar en acuerdo con la ciencia real a la que se trata de comprender. Notamos que los puntos (i) y (iii) son XLIII los más conflictivos y alejados de la realidad de la teoría de estabilidad. Consideremos estos aspectos en más detalle. Por ejemplo, tomemos un científico cuya práctica de investigación está centrada en la teoría clásica, y le interesa principalmente evaluar cargas criticas clásicas en sistemas no clásicos, como elementos estructurales construidos con materiales compuestos (composites). Un artículo que deba ser revisado por otro científico inmerso en la teoría poscrítica encontrará que sólo le están contando parte de la historia, y que el estudio es preliminar y está incompleto. Pero no desechará la información provista por errónea, sino por incompleta y que puede llevar a conclusiones equivocadas. Tampoco ambos científicos viven en mundos conceptuales diferentes, porque muy probablemente ambos conozcan acerca de los dos paradigmas, sino que su práctica transita por caminos que terminan en lugares diferentes. Lo que para el primer científico es “trabajo a ser realizado en un futuro”, para el segundo es “trabajo aún no realizado”. Sobre los científicos que generan el nuevo paradigma Este es un tema marginal en Kuhn, pero el caso de Koiter parece corresponderse bien con el siguiente párrafo de Kuhn: “Casi siempre, los hombres que realizan esos inventos fundamentales de un nuevo paradigma han sido muy jóvenes o muy noveles en el campo cuyo paradigma cambian… se trata de hombres que, al no estar comprometidos con las reglas tradicionales de la ciencia normal debido a que tienen poca práctica anterior, tiene muchas probabilidades de ver que esas reglas no definen ya un juego que pueda continuar adelante y de concebir otro conjunto que pueda reemplazarlas” (Kuhn, 1962, pp. 146-147). La situación de Koiter al buscar su tema de tesis fue descripta así por él mismo: “Llegué a la conclusión que valía la pena escribir una tesis doctoral en las noches… Al año siguiente imaginé que había encontrado una base adecuada, el teorema que el dominio estable en el espacio de carga de una estructura elástica con un estado precrítico lineal es siempre convexo. Fue desalentador cuando descubrí algo mas tarde que Papkovich había publicado este teorema en 1934…” (Koiter, 1979, pp. 243). Esto ilustra que Koiter era un recién llegado al campo y no tenia el tipo de compromiso con las reglas tradicionales de la teoría clásica. Aunque no se trata de algo central en la visión de Kuhn, el papel que cumplen los forjadores de un paradigma aparece acertadamente descripto en nuestro caso. LA VISIÓN DE LOS PROGRAMAS DE INVESTIGACIÓN DE LAKATOS Podemos analizar el cambio teórico de la teoría clásica a la de Koiter desde el punto de vista de los programas de investigación. Siguiendo a Lakatos (1978), podemos decir que existió un programa de investigación regresivo, basado en el concepto de carga crítica clásica, el cual fue progresivo en el momento en que se aplicó solamente a columnas y placas, pero que se convirtió en regresivo al abordar problemas de algunas cáscaras. Hay un cambio racional, y está basado en el poder explicativo del nuevo programa. XLIV El enfoque de Lakatos permite una mejor caracterización de la estructura de los programas con respecto a la caracterización indefinida de la estructura de los paradigmas en Kuhn. El núcleo firme Según Lakatos, en el núcleo firme se define el conocimiento fundamental no problemático, las leyes básicas del programa. En el núcleo firme del programa de Koiter, los postulados básicos son (a) Los axiomas de equilibrio y estabilidad de sistemas elásticos, basados en la energía potencial total. Estos axiomas no pueden someterse a cuestionamiento porque están tomados como el núcleo que se va a defender. Tampoco pueden demostrarse de manera independiente. Como sustento requieren de usar trabajos virtuales para sistemas continuos, y no tienen ni ese apoyo para sistemas discretos. (b) La estabilidad del sistema en el estado crítico (que se calcula en base a derivadas superiores de la energía) determina si la trayectoria poscrítica en su parte inicial (desplazamientos muy pequeños) existe para valores crecientes de la carga o sólo para valores decrecientes. Koiter señala esto así: “Esto lleva a la sospecha que la diferencia en el comportamiento elástico de diferentes estructuras con cargas cercanas a la carga teórica de pandeo esta conectado con el carácter diferente de los posibles estados de equilibrio vecinos correspondientes a esas cargas” (Koiter, 1945, pp. 5). (c) Para pequeñas irregularidades en el sistema el estado precrítico se perturba y da una carga máxima (menor que la crítica cuando el estado crítico mismo es inestable) que se puede evaluar mediante un análisis de perturbación del comportamiento perfecto. El cinturón protector Las hipótesis auxiliares que defienden el núcleo se construyen de manera ecléctica. En la versión de Koiter, la teoría de estabilidad elástica incluye un cinturón protector constituido por varios elementos: (a) Se considera que las componentes estructurales más eficientes son de una dimensión o de dos dimensiones, con tensiones aproximadamente constantes en la sección transversal o en el espesor (estado membranal), para los que el pandeo ocurre de manera de bifurcación. (b) Se considera que se puede usar el tensor de Cauchy de tensiones conjuntamente con el tensor de deformaciones de Green-Lagrange, lo cual es estrictamente inconsistente. Pero según Koiter, “En muchos problemas de pandeo podemos ignorar la diferencia entre las coordenadas cartesianas en la estructura indeformada y en el estado fundamental como variables independientes” (Koiter, 1982). (c) Koiter usa una teoría simplificada de cáscaras, para cáscaras rebajadas: XLV “Para cáscaras el comportamiento mas característico de pandeo ocurre en modos de pandeo rebajados, cuya longitud de onda mínima L es pequeña comparada con el radio de curvatura más pequeño de la superficie media” (Koiter, 1982). Estas hipótesis auxiliares que hace Koiter podrían ser removidas si hiciera falta, pero a él le parecen razonables. Lejos de ser parte del núcleo central, estas condiciones pueden ser atacadas por otros autores y podrían estar sujetas a ajustes sin perjuicio del núcleo central. La heurística La heurística es la maquinaria para la solución de problemas en la teoría. Se ayuda de técnicas matemáticas y consiste en reglas metodológicas. La heurística positiva avanza sin importarle lo que dice la evidencia en contra, como los resultados adversos del cilindro elíptico o del cilindro con agujeros. Como heurística importante la nueva teoría usa la técnica de perturbaciones. Thompson y otros investigadores enriquecen la heurística al asumir sistemas con múltiples grados de libertad (Thompson y Hunt, 1973), de modo que incorporan al método de elementos finitos como técnica de solución. El cambio de programas En el enfoque de Lakatos el cambio de programa de investigación comienza cuando el viejo programa se vuelve regresivo, o sea cuando la teoría se comienza a fabricar para acomodarse a los hechos. Se manufacturan hipótesis auxiliares después de los acontecimientos para proteger a la teoría de los hechos. Se atrasa con relación a los hechos y el programa regresivo corre detrás de los hechos para alcanzarlos. Esta situación regresiva se encuentra fácilmente en la teoría clásica de estabilidad, lo cual pone en evidencia una gran desconfianza en sus postulados y predicciones. La teoría de Koiter por el contrario, es progresiva. Explica los fenómenos no explicados en la teoría anterior, y conduce a descubrir hechos o fenómenos nuevos. Por ejemplo, conduce a descubrir el acoplamiento de modos, ignorado hasta ese momento. El nuevo programa logro predecir hecho nuevos muy rápidamente una vez que fue aceptado por un grupo significativo (aunque no completo ni mayoritario) de científicos. La historia externa La historia en Lakatos contiene una historia interna y una externa. Lo que hemos narrado anteriormente es parte de la historia interna, formada por la explicación racional del crecimiento del conocimiento objetivo. La historia externa es la historia sociológica y social de la ciencia. Aquí interesa fundamentalmente considerar la participación de Koiter, que produjo un cambio en la perspectiva desde la cual se podía ver el problema de estabilidad. Afortunadamente la situación de Koiter se encuentra documentada en sus escritos (Koiter, 1979) y en las conferencias que dictó en Río de Janeiro en 19831. ______________________________ 1 Tuvimos ocasión de participar en dos cursos dictados por Koiter en LNCC en 1983 y 1985. XLVI “En la primavera de 1940 tuve la mala fortuna de caer con neumonía y pleuresía y casi no pude salir de cama cuando ocurrió la invasión Nazi el 10 de mayo. Sin embargo, en cama leí un artículo estimulante por Leslie Cox… y su tratamiento simple del comportamiento de una columna con un apoyo no lineal elástico me sugirió la idea básica que la inestabilidad en la carga crítica podría ser la explicación del desastroso efecto de imperfecciones. Esta conjetura me llevó al desarrollo de la teoría general de estabilidad elástica no lineal en mi tesis… El trabajo básico, incluyendo la aplicación del sorprendente problema de pandeo de cáscaras cilíndricas bajo compresión axial, fue completado en febrero de 1942” (Koiter, 1979, pp. 243). El idioma en el cual fue escrita la tesis sin duda influyó en sus posibilidades de impacto: “Debido a que el alemán era la única lengua extranjera permitida por los Nazis para publicaciones, mi manuscrito obviamente sólo podía ser escrito en mi lengua nativa, que no era fácilmente accesible a la mayoría de mis colegas en el extranjero” (Koiter, 1979, pp. 243). La defensa de la tesis fue postergada por Koiter hasta la finalización de la guerra en 1945. La tesis fue publicada por un editor a quien Koiter estuvo agradecido hasta su retiro, porque le facilitó demorar la publicación hasta que se produjo el fin de la guerra. La primera presentación que realizó Koiter sobre estabilidad fue en una conferencia en París en 1946. El tema del trabajo era el pandeo de placas en estados poscríticos avanzados, pero sin recapitular la teoría que ya había desarrollado. Al parecer, Koiter entendía que ya había publicado su teoría en la tesis, y que no correspondía reiterar lo dicho otra vez. Las dificultades de entender la teoría misma, sumado a que estaba presentando un tópico que avanzaba sobre la teoría, hizo que el trabajo no fuera bien recibido: “La sesión del congreso en la que presenté un trabajo con algunos resultados numéricos inesperados fue coordinada por von Mises, quien … cerró la discusión diciendo que el no creía una palabra del trabajo” (Koiter, 1979, pp. 244). Con esta mala recepción, Koiter se desanimó y se retiró de este campo, al que sólo volvería para dictar un curso en Estados Unidos en 1961. El primer trabajo sobre estabilidad publicado por Koiter en inglés es de 1956 (Koiter, 1956). La primera traducción de su tesis doctoral al inglés fue publicada por NASA en 1967, pero para esa época había otros científicos trabajando en los pasos de Koiter. Dos escuelas siguieron a Koiter: la de Harvard, con Budianski y Hutchinson, quienes continuaron con la formulación continua, y la de Inglaterra (centrada en University College London) donde se desarrolló la formulación discreta con Thompson y Chilver. Koiter mismo no desarrolló una escuela en su entorno: “Una de las serias limitaciones de mi carrera fue que he acompañado sólo unos pocos estudiantes a su grado doctoral… Una razón … es que en mi trabajo no tenía mucha necesidad de asistencia por jóvenes asociados” (Koiter, 1979, pp. 240). XLVII La escuela de Harvard fue también pequeña, pero en University College London se llevó a cabo un programa extenso de investigación, extendiendo la teoría entre 1965 y 1985. Si bien la formulación discreta permite la incorporación del método de elementos finitos a la teoría, esto sólo se realizo en la década de los 80. La tesis doctoral de Thompson en Cambridge data de 1963. En el prólogo de su primer libro, Thompson argumenta que su formulación fue desarrollada independientemente de la de Koiter: “Por varios años el primer autor no tuvo conocimiento de la disertación clásica del Prof. W. T. Koiter, la cual había permanecido desconocida desde 1945 y sólo recientemente fue traducida al inglés por la NASA. Esto fue muy afortunado, porque el peso de la contribución del Prof. Koiter podría haberlo desalentado a seguir con su propio desarrollo en el tema” (Thompson y Hunt, Prólogo, 1973) Koiter menciona acerca de las influencias que operó su trabajo en otros investigadores: “El interés en este campo también floreció en ese tiempo en particular en la Universidad de Harvard, donde creo que mi trabajo ha tenido alguna influencia, y en University College en Londres, donde un enfoque similar para sistemas elásticos discretos fue desarrollado de manera mas o menos independiente, como se describe tan elocuentemente en el prefacio de la monografía de Thompson y Hunt…” (Koiter, 1979, pp. 244). La historia externa explica porqué el trabajo de Koiter permaneció sin conocerse entre 1945 y 1961, y sólo con muchas restricciones a partir de ese momento. Las dificultades teóricas asociadas a la teoría misma fueron un escollo a su divulgación generalizada, que siempre permaneció limitada a un grupo de estudiosos que podían dedicar el tiempo necesario para su comprensión. EL CAMBIO EPISTEMOLOGICO EN LA TEORÍA DE ESTABILIDAD Una de las utilidades del enfoque epistemológico es que nos ayuda a seguir aspectos de las teorías que de otra forma podrían pasarnos desapercibidos. En este caso hemos prestado atención a dos enfoques de la filosofía de la ciencia, asociados a la interpretación de paradigmas científicos y a la de programas de investigación. Algunas de las conclusiones importantes que surgen de esta mirada pueden resumirse de la siguiente manera. (a) Resulta útil visualizar de una manera más general las teorías dentro del marco de paradigmas o programas. La riqueza descriptiva de los programas de investigación parece más adecuada para las teorías de las ciencias de la ingeniería, al incluir una estructura explícita. Esa estructura explícita (núcleo, cinturón, heurística) es además identificable en el caso de las teorías de estabilidad. El concepto de paradigma es más elusivo y no nos ayuda tanto a estructurar la teoría analizada. (b) Entendemos que las crisis de las teorías en ciencias de la ingeniería se generan cuando se identifican sus límites y se encuentran problemas que no pueden predecir correctamente un comportamiento importante. Pero no porque el problema sea conceptualmente crucial (como pretendía Bacon y los empiristas) o porque se haya identificado una forma de falsación, como pretendía Popper (1969), sino porque la limitación encontrada es significativa en el contexto de XLVIII aplicación. Por eso la teoría clásica de estabilidad entró en crisis, al encontrar serias limitaciones en problemas significativos (cilindro con carga axial, significativo en la industria aeronáutica). (c) El papel de las anomalías en el cambio de teoría aparece ilustrado en nuestro estudio de estabilidad. El problema del cilindro bajo carga axial, ¿fue planteado como un caso de falsación, en el sentido de Popper? Claramente no. Nadie diseñó ese caso como un experimento crucial con la intención de falsar la teoría. Como menciona Timoshenko (1936), se debió al uso de cáscaras delgadas en estructuras aeronáuticas, que necesitaban de un nivel de seguridad alto y por ello indujeron a los ingenieros a realizar experimentos para tener confirmaciones independientes de los valores teóricos. La sorpresa fue encontrar diferencias tan grandes entre experimentos y cálculos. El motor de curiosidad fue la demanda de una industria, ampliando las fronteras de las necesidades, las que llevaron a pasar de columnas a cáscaras como tema de interés. Sin embargo, cuando Kempner encontró falencias en la teoría de Koiter (el problema del cilindro elíptico en compresión), esta no entra en crisis porque el problema no es significativo como necesidad industrial, sino sólo es un contraejemplo y puede ser tratado como una anomalía. En definitiva, se genera una hipótesis ad-hoc (la teoría no puede aplicarse en ese tipo de casos). En las ingenierías el conocimiento está atado a su significación en cuanto a las necesidades que logra satisfacer. Eso hace que necesariamente requiera de un marco histórico y uno de aplicación. El conocimiento no puede separarse de la aplicación, porque sino deja de tener significación. (d) El periodo de transición juega un papel fundamental en el cambio teórico, no tanto porque los investigadores involucrados acumulen conocimientos hasta encontrar una nueva formulación, sino porque permite incorporar términos y conceptos nuevos útiles en la nueva teoría, aunque de una manera diferente. En nuestro ejemplo la transición aparece similar a lo descripto por Lakatos. (e) El lugar de las revoluciones ha sido siempre conflictivo en la nueva filosofía de la ciencia. En nuestro caso hubo un cambio revolucionario; sin embargo ese cambio no tuvo la forma de una conversión en masa al nuevo paradigma, con la desaparición del viejo paradigma. Por el contrario, han seguido coexistiendo ambos paradigmas, aunque dentro de un marco mas general en el que se reconocen las limitaciones del paradigma viejo. Esto es evidente en los programas para propósitos generales de elementos finitos, en los que coexisten los algoritmos de calculo de carga crítica con los de evaluación de trayectorias no lineales que tiene sentido en la interpretación de Koiter. AGRADECIMIENTOS Este trabajo no habría sido posible sin el aporte de los colegas y profesores en University College London durante el periodo de 1975-1979. También agradecemos las enseñanzas de Koiter durante 1983 y 1985 en Río de Janeiro, y los comentarios que realizó en reuniones más informales. XLIX REFERENCIAS Almroth, B., 1963, "Postbuckling behavior of axially compressed circular cylinders", AIAA Journal, vol. 1, pp. 630. Bryan, G. H., 1888, “On the stability of elastic systems”, Proceedings of the Cambridge Philosophical Society, vol. 6, pp. 199. Bushnell, D., 1985, "Computerized buckling analysis of shells", Martinus Nijjhoff, Dordrecht. Cox, H. L., 1940, “Stress analysis of thin metal construction”, Journal of the Royal Aeronautical Society, vol. 44, pp. 231. Donnell, L. H., 1976, "Beams, plates and shells", McGraw-Hill, Londres. Esslinger, M. y Geier, B., 1975, "Postbuckling behaviour of structures", Springer, Berlin. Godoy, L. A., 2000, "Theory of elastic stability: Analysis and sensitivity", Taylor and Francis, Filadelfia. Hoff, N. J., Madsen, W. 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Acta Mechanica 1 11 31 47 61 85 101 121 129 141 159 179 189 215 233 Magnetoelastic coupling on soft ferromagnetic solids with an interface crack On stability domains of nonconservative systems under small parametric excitation The fast spinning motion of a rigid body in the presence of a gyrostatic momentum Nonlinear investigation of the possibility to exceed the critical speed by a load on a string A general framework for generating convex yield surfaces for anisotropic metals An intermediate crack model for aws in piezoelectric solids Path-independent integral analyses for microcrack damage in dissimilar anisotropic materials Summation of perturbation solutions to nonlinear oscillations Finite element analysis of thermopiezoelectric smart structures An electromechanically coupled theory for piezoelastic beams taking into account the charge equation of electrostatics Similarity analysis of strong converging spherical shock waves in radiating gas In-plane problem for wave propagation through elastic solids with a periodic array of cracks The eect of temperature on the viscoelastic response of rubbery polymers at nite strains A study of liquid evaporation on forced convection in porous media with nondarcy eects A note on the series solution of the solitary wave problem 154(1-4) 2002 Wei L. Yapeng S. Daining F. Mailybaev AA. Ismail AI. Amer TS. Gavrilov S. Mollica F. Srinivasa AR. Dascalu C. Homentcovschi D. Tian WY. Chen YH. Wu B. Zhong H. Gornandt A. Gabbert U. Krommer M. Irschik H. Hirschler T. Gretler W. Scarpetta E. Drozdov AD. Dorfmann A. Shih MH. Huang MJ. Engevik L. AIAA Journal 2033 2042 Optimized nonuniform rational b-spline geometrical representation for aerodynamic design of wings Active and passive suppressions of nonlinear panel utter using nite element method 39(11) 2001 Lepine J. Guibault F. Trepanier JY. Pepin F. Moon SH. Kim SJ. 2 2051 2121 2131 Coupled analytical sensitivity analysis and optimization of three-dimensional nonlinear aeroelastic systems Aeroacoustic characterization, noise reduction, and dimensional scaling eects of high subsonic jets Discontinuous spectral element solution of acoustic radiation from thin airfoils Spatial linear instability of conuent wake/boundary layers Implicit weighted essentially nonoscillatory schemes for the compressible navierstokes equations Initial relaxation of spatially evolving turbulent channel ow with blowing and suction Inow conditions in stochastic eulerian-lagrangian calculations of two-phase turbulent ow Higher-order solution procedure for three-dimensional nonideal magnetogasdynamics Stability of acoustic wave in two-phase dilute ow with mass transfer Shock-wave/turbulent boundary-layer interactions in nonequilibrium ows 2141 Eective test time evaluation in high-enthalpy expansion tube 2148 2158 Half model restrictions for linear plug nozzle testing Time-discontinuous stabilized space-time nite elements for timoshenko beams 2168 Required relationship between objective function and pareto frontier orders: practical implications Fast-response cylindrical air bearing balance Probe diagnostics of gas discharges in supersonic airows 2062 2070 2076 2082 2091 2100 2111 2175 2180 2188 2192 2198 2206 2216 2218 2223 2225 2227 Free vibrations of an orthotropic thin cylindrical shell on a pasternak foundation Stochastic nite element analysis of beam with statistical uncertainties Exact and accurate solutions in the approximate reanalysis of structures Detection of multiple damages by prestack reverse-time migration Advanced algebraic model for turbulent diusion vector in two-equation turbulence models Parallel performance analysis of fvtd computational electromagnetics code Prediction of separation angles induced by sharp ns with attack angle Dynamics of an orbiting exible beam with a moving mass Cyclic creep of piezoelectric polymer polyvinylidene uoride Maute K. Nikbay A. Farhat C. Simonich JC. Narayanan S. Barber TJ. Nishimura M. Rasetarinera P. Kopriva DA. Hussaini MY. Liou WW. Liu FJ. Yang JY. Perng YC. Yen RH. Chung YM. Sung HJ. Yang JC. Chang KC. Gaitonde DV. Daniel E. Thevand N. Grasso F. Marini M. Ranuzzi G. Cuttica S. Chanetz B. Sasoh A. Ohnishi Y. Ramjaun D. Takayama K. Otsu H. Abe T. Wisse MEN. Bannink WJ. Grohmann BA. Wallmersperger T. Kroplin BH. Dornberger R. Messac A. Ismail-Yahaya A. Magill JC. Hinds MF. Malonson MR. Ershov A. Ardelyan N. Chuvashev S. Shibkov V. Timofeev I. Paliwal DN. Pandey R. Ishida R. Kirsch U. Papalambros PY. Lin X. Yuan FG. Abe K. Camberos JA. White MD. Koide S. Oguamanam DCD. Hansen JS. Heppler GR. Vinogradov AM. Schumacher SC. AIAA Journal 2233 2242 2250 2255 2262 2268 2278 2283 2293 Kriging models for global approximation in simulation-based multidisciplinary design optimization Detection and repair of poorly converged optimization runs 2302 Evaluation of damage tolerance analysis tools for lap joints Far-eld calculations for turbofan noise Drag coeÆcient reduction in the presence of pressure gradients by heat transfer Numerical simulation of jets in a crossow using dierent turbulence models Blended ausm plus method for all speeds and all grid aspect ratios Large-eddy simulation of supersonic compression-ramp ow by high-order method Modeling of controlled shock-wave/boundary-layer interactions in transonic channel ow Two-point descriptions of wake turbulence with application to noise prediction 2308 2320 2327 2336 Fuel-air mixing enhancement by synthetic microjets Capillary ow in containers of polygonal section Spacelab experiments on combustion of heptane/hexadecane droplets Microgravity ignition delay of solid fuels in low-velocity ows 2343 2351 2357 2366 Unsteady dynamic variables method for heterogeneous solid propellant burning Chemistry of jp-10 ignition Numerical analysis of reducing driver gas contamination in impulse shock tunnels Suppression of self-sustained oscillations in a supersonic impinging jet 2374 2382 2389 2394 Active-control system for breakup of airplane trailing vortices Multibody system analysis based on hamilton's weak principle Anisotropic thin-walled beams with closed cross-sectional contours Precise time-integration method with dimensional expanding for structural dynamic equations 39(12) 2001 Simpson TW. Mistree F. Kim H. Papila M. Mason WH. Haftka RT. Watson LT. Grossman B. Trego A. Cope D. Roy ID. Eversman W. Feiler C. Keimasi MR. Taeibi-Rahni M. Vierendeels J. Merci B. Dick E. Rizzetta DP. Visbal MR. Gaitonde DV. Benay R. Berthouze P. Bur R. Devenport WJ. Muthanna C. Ma RL. Glegg SAL. Wang H. Menon S. Weislogel MM. Shaw BD. Clark BD. Wang DF. Roslon M. Olenick S. Zhou YY. Walther DC. Torero JL. Fernandez-Pello AC. Ross HD. Surzhikov ST. Krier H. Li SC. Varatharajan B. Williams FA. Burtschell Y. Cardoso M. Zeitoun DE. Elavarasan R. Krothapalli A. Venkatakrishnan L. Lourenco L. Crouch JD. Miller GD. Spalart PR. Kunz DL. Johnson ER. Vasiliev VV. Vasiliev DV. Gu YX. Chen BS. Zhang HW. Guan ZQ. 2400 2402 Diusion timescale of porous pressure-sensitive paint Evaluation of turbulence-model performance in jet ows 2404 2406 2409 2411 2414 EÆcient method for calculating wall proximity Improved rhie-chow interpolation for unsteady ow computations Side force on an ogive cylinder: eects of freestream turbulence Turbulence in wake of a self-propelled body with and without swirl Geometries for ve-hole-type probes with planar sensor arrays 2417 Accurate calibration of low-speed wind tunnels, including humidity and compressibility Full-eld experimental investigations on resonant vibration of cracked rectangular cantilever plates Static and dynamic validations of a rened thin-walled composite ream model Unied formulation for compressible-incompressible ow simulation with mesh adaptation 2419 2422 2425 Liu TS. Teduka N. Kameda M. Asai K. Woodru SL. Seiner JM. Hussaini MY. Erlebacher G. Boger DA. Shen WZ. Michelsen JA. Sorensen JN. Luo SC. Lua KB. Lim TT. Goh EKR. Sirviente AI. Patel VC. Babinsky H. Kuschel U. Hodson HP. Moore DF. Welland ME. Covert EE. Durgin FH. Ma CC. Hsieh DM. Qin ZM. Librescu L. Turgeon E. Pelletier D. AIAA Journal 16 26 33 42 50 58 67 74 82 91 105 117 126 137 147 154 162 170 172 175 177 179 181 185 Turbulence ingestion noise, part 1: experimental characterization of gridgenerated turbulence Turbulence ingestion noise, part 2: rotor aeroacoustic response to grid-generated turbulence Three-dimensional numerical simulation of the jet screech phenomenon Transducer for direct measurement of skin friction in hypervelocity impulse facilities Study of direct-measuring skin-friction gauge with rubber sheet for damping Relaxation of turbulent boundary layer submitted to sudden distortion at the wall Numerical simulation of the interaction of microactuators and boundary layers Magnetohydrodynamic control of hypersonic ows and scramjet inlets using electron beam ionization Nonlinear ltering for low-velocity gaseous microows Higher-order piezoelectric plate theory derived from a three-dimensional variational principle Rened structural model for thin- and thick-walled composite rotor blades Response and failure characteristics of internally pressurized elliptical composite cylinders Fuzzy nite element method for frequency response function analysis of uncertain structures Rened plate theory and its variants Design optimization of springback in a deepdrawing process Displacement-based optimization for truss structures subjected to static and dynamic constraints Thermal buckling of functionally graded plates Models of secondary vorticity evolution during normal vortex-cylinder interaction Two-step method for static topological reanalysis Assessment of local blowing and suction in a turbulent boundary layer Surface-shear-stress pulses in adverse-pressure-gradient turbulent boundary layers Inuence of the wall condition on k-omega turbulence model predictions Turbulent ow of power-law uids through circular pipes Periodic vibration of plates with large displacements 40(1) 2002 Wojno JP. Mueller TJ. Blake WK. Wojno JP. Mueller TJ. Blake WK. Shen H. Tam CKW. Goyne CP. Stalker RJ. Paull A. Magill S. MacLean M. Schetz J. Kapania R. Sang A. Pulliam W. Bouda NN. Benabid T. Fulachier L. Lockerby DA. Carpenter PW. Davies C. Macheret SO. Shneider MN. Miles RB. Kaplan CR. Oran ES. Batra RC. Vidoli S. Jung SN. Nagaraj VT. Chopra I. McMurray JM. Hyer MW. Moens D. Vandepitte D. Shimpi RP. Choi KK. Kim NH. Missoum S. Gurdal Z. Javaheri R. Eslami MR. Marshall JS. Lian HD. Yang XW. Chen SH. Kim K. Sung HJ. Chung MK. Sandborn VA. Thivet F. Daouk M. Knight DD. Warsi ZUA. Ribeiro P. AIAA Journal 193 199 209 217 227 235 244 Mean ow features around the inline wheels of four-wheel landing gear Wall-normal-free reynolds-stress model for rotating ows applied to turbomachinery [review] Role of actuation frequency in controlled ow reattachment over a stalled airfoil Three-dimensional rectangular duct code with application to impedance eduction Study of the error and eÆciency of numerical schemes for computational aeroacoustics Computation of ow noise using source terms in linearized euler's equations Unsteady ow evolution in porous chamber with surface mass injection, part 2: acoustic excitation 3 40(2) 2002 Lazos BS. Gerolymos GA. Vallet I. Amitay M. Glezer A. Watson WR. DeBonis JR. Scott JN. Bogey C. Bailly C. Juve D. Apte S. Yang V. 4 254 267 276 285 293 301 310 319 327 334 340 346 359 368 376 382 389 391 393 Predictions of transitional ows in low-pressure turbines using intermittency transport equation Aperture eects on the aerooptical distortions produced by a compressible shear layer Numerical investigation of turbulent mixing in a jet/wake vortex interaction Vortex structure on a delta wing at high angle of attack Nonlinear uctuation-dissipation theory to the second order Analytical and computational aspects of collaborative optimization for multidisciplinary design Diode laser-driven microthrusters: a new departure for micropropulsion Dynamic analysis of exible beams undergoing overall motion employing linear strain measures Model reduction for dynamical systems with local nonlinearities Teleoperation of a truss structure by force command in ets-vii robotics mission Buckling of composite plates with local damage and thermal residual stresses Prediction of compressive failure in laminated composites at room and elevated temperature Large-scale structural analysis by parallel multifrontal solver through internetbased personal computers EÆcient method for dynamic condensation of nonclassically damped vibration systems Multiobjective topology optimization of a beam under torsion and distortion Structural optimization with frequency constraints using the nite element force method Shape optimization of transonic compressor blade using quasi-three-dimensional ow physics Semistructured grid generation in three dimensions using a parabolic marching scheme Evaluation of nite element predictions of analog specimen residual stress bondline failures Suzen YB. Xiong G. Huang PG. Fitzgerald EJ. Jumper EJ. Gago CF. Brunet S. Garnier F. Ozgoren M. Sahin B. Rockwell D. Ali AH. Alexandrov NM. Lewis RM. Phipps C. Luke J. Seo S. Yoo HH. Qu ZQ. Nohmi M. Matsumoto K. de Almeida SFM. Hansen JS. Ahn J. Waas AM. Kim SJ. Lee CS. Kim JH. Qu ZQ. Selvam RP. Kim TS. Kim YY. Sedaghati R. Suleman A. Tabarrok B. Chung J. Lee KD. Thompson DS. Soni BK. Richardson DE. Hoskins BR. Crook RA. AIAA Journal 401 408 419 430 438 443 450 456 465 474 481 490 497 501 510 517 526 531 537 545 553 559 566 576 579 582 Aerodynamics of a jet in the vortex wake of a wing Computational study of intake duct eects on fan utter stability Experimental and theoretical study of gust response for high-aspect-ratio wing High subsonic jet experiments: turbulence and noise generation studies Quantitative interferometry in the severe acoustic environment of resonant supersonic jets Applications of high-order optimized upwind schemes for computational aeroacoustics Parallel computation of forward radiated noise of ducted fans with acoustic treatment Noise from ne-scale turbulence of nonaxisymmetric jets Aeroacoustics of wall-bounded turbulent ows Numerical simulation of two-dimensional blade-vortex interactions using unstructured adaptive meshes Experiments on passive hypervelocity boundary-layer control using an ultrasonically absorptive surface Direct surface triangulation using stereolithography data Improvements in parallel chimera grid assembly Parametric study of heat release preceding a blunt body in hypersonic ow Two-dimensional synthetic jet simulation Dynamics of slender bodies separating from rectangular cavities Harmonic perturbations in turbulent wakes Neural network detection of shockwaves Turbulence models in pulsating ows EÆcient uncertainty analysis methods for multidisciplinary robust design Asymptotic theory for laminated piezoelectric circular cylindrical shells Feasible region in general design space of lamination parameters for laminated composites Residual strength prediction of aircraft fuselages using crack-tip opening angle criterion Rise of total pressure near the stagnation point on a sphere Symmetry properties of the transitional sphere wake New self-referencing pressure-sensitive-paint measurement 40(3) 2002 Wang FY. Zaman KBMQ. Vahdati M. Sayma AI. Breard C. Imregun M. Tang DM. Dowell EH. Narayanan S. Barber TJ. Polak DR. Mercer CR. Raman G. Zhuang M. Chen RF. Ozyoruk Y. Tam CKW. Pastouchenko NN. Hu ZW. Morfey CL. Sandham ND. Oh WS. Kim JS. Kwon OJ. Rasheed A. Hornung HG. Fedorov AV. Malmuth ND. Ito Y. Nakahashi K. Prewitt NC. Belk DM. Shyy W. Takaki R. Liou MS. Lee CY. Goldstein DB. Shalaev VI. Fedorov AV. Malmuth ND. Reau N. Tumin A. Berdahl C. Scotti A. Piomelli U. Du XP. Chen W. Cheng ZQ. Reddy JN. Diaconu CG. Sato M. Sekine H. Chen CS. Wawrzynek PA. Ingraea AR. Williams JC. Mittal R. Wilson JJ. Najjar FM. Subramanian CS. Amer TR. Oglesby DM. Burkett CG. 585 586 Quasi-failure analysis on resonant demolition of random structural systems Topology optimization for maximum natural frequency using simulated annealing and morphological representation Applied Mathematical Modelling 89 113 141 Dem modelling of industrial granular ows: 3d case studies and the eect of particle shape on hopper discharge Numerical modelling of free surface ows in metallurgical vessels Numerical simulation of solids ow in a blast furnace 155 171 191 Erosion prediction in slurry pipeline tee-junctions Flow modelling in casting processes Tube erosion modelling in a uidised bed 203 Analysis of performance of an iron-bath reactor using computational uid dynamics Predicting gas-liquid ow in a mechanically stirred tank The issue of numerical uncertainty Fluid ow and gas-liquid mass transfer in gas-injected vessels Developments in modelling of gas injection and slag foaming Cfd modelling of thickeners at worsley alumina pty ltd Prediction of dust loss from conveyors using computational uid dynamics modelling Finite volume methods applied to the computational modelling of welding phenomena An experimental and numerical cfd study of turbulence in a tundish container 223 237 249 263 281 297 311 323 337 351 Cfd, a design tool for a new hot metal desulfurization technology Recent applications of cfd modelling in the power generation and combustion industries 26(2 Special Issue SI) 2002 Cleary PW. Sawley ML. Liovic P. Rudman M. Liow JL. Zhang SJ. Yu AB. Zulli P. Wright B. Austin P. Brown GJ. Cleary P. Ha J. Alguine V. Nguyen T. Achim D. Easton AK. Schwarz MP. Witt PJ. Zakhari A. Panjkovic V. Truelove J. Ostrovski O. Lane GL. Schwarz MP. Evans GM. Freitas CJ. Taniguchi S. Kawaguchi S. Kikuchi A. Guo DC. Gu L. Irons GA. Kahane R. Nguyen T. Schwarz MP. Witt PJ. Carey KG. Nguyen TV. Taylor GA. Hughes M. Strusevich N. Pericleous K. Gardin P. Brunet M. Domgin JF. Pericleous K. Pirker S. Gittler P. Pirker H. Lehner J. Stopford PJ. Applied Mathematical Modelling 377 397 421 449 473 On coupling electromagnetic elds and lumped circuits with tlm Multi-domain mass conservative dual reciprocity method for the solution of the non-newtonian stokes equations Solidication modelling with a control volume method on domains subjected to viscoplastic deformation A numerical and experimental investigation of the modeling of microwave heating for liquid layers using a rectangular wave guide (eects of natural con vection and dielectric properties) Peakons of the camassa-holm equation 26(3) 2002 Mariani AJ. Kirkup SM. Huang Y. Jones GR. Florez WF. Power H. Davey K. Rodriguez NJ. Ratanadecho P. Aoki K. Akahori M. Liu ZR. Qian TF. Applied Mathematics & Mechanics (English Edition) 1231 1240 1252 1260 1268 1273 1279 1291 1301 1306 1311 New principles of work and energy as well as power and energy rate for continuum eld theories Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear nance system(i) Research on the inelastic seismic responses of shear-type multistory buildings with regular asymmetry New bifurcation patterns in elementary bifurcation problems with single-side constraint Investigation of random response of rotational shell when considering geometric nonlinear behaviour Boundedness and uniform boundedness results for certain non-autonomous differential equations of fourth order An edge crack problem in a semi-innite plane subjected to concentrated forces Predicting the consequences of seawater intrusion and protection projects Chaos in perturbed planar non-hamiltonian integrable systems with slowlyvarying angle parameters Ishikawa iterative process in uniformly smooth banach spaces A mode-ii griÆth crack in decagonal quasicrystals 5 Zhang YM. Liu QL. Wen BC. Cui GY. Tai K. Wang BP. 22(11) 2001 Dai TM. Ma JH. Chen YS. Cai XH. Wu RF. Xu SB. Wu ZQ. Chen YS. Gao SQ. Jin L. Niemann HJ. Liu HP. Tunc C. Chen YZ. Hasebe N. Yuan YR. Liang D. Rui HX. Chen LQ. Huang ZY. Guo YC. Fan TY. 6 1318 1325 1333 1344 1352 The bounds of the general m and j sets and the estimations for the hausdor's dimension of the general j set Analytic sensitivity analysis for shape optimization The smooth and nonsmooth travelling wave solutions in a nonlinear wave equation The analysis of dynamic stress intensity factor for semi-circular surface crack using time-domain bem formulation The extinction behavior of the solutions for a class of reaction-diusion equations Liu XD. Yan DJ. Zhu WY. Wang GX. Zhang DX. Jiang YZ. Cai J. Li SM. Zhong M. Zhang YY. Chen SL. Applied Mathematics & Mechanics (English Edition) 1357 1368 1375 1383 1390 1397 1404 1410 1422 1429 1436 1446 1458 1468 1476 Unied way for dealing with three-dimensional problems of solid elasticity Complex inner product averaging method for calculating normal form of ode Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear nance system(ii) New principles of power and energy rate of incremental rate type for generalized continuum eld theories Interval arithmetic and static interval nite element method A xed point theorem for set-valued mappings Weighted solution of small-deection buckling equation of thin shell Study on dynamics, stability and control of multi-body exible structure system in functional space Continuation method applied in kinematics of parallel robot Self-similar solutions of fracture dynamics problems on axially symmetry Stability analysis of maxwell viscoelastic pipes conveying uid with both ends simply supported Linear and nonlinear aerodynamic theory of interaction between exible long structure and wind Iterative process for certain nonlinear mappings with lipschitz condition General expressions of constitutive equations for isotropic elastic damaged materials Existence and multiplicity of positive solutions for a fourth-order p-laplace equations 22(12) 2001 Xu Q. Sun HC. Chen YS. Sun HJ. Ma JH. Chen YS. Dai TM. Guo SX. Lu ZZ. Banerjee A. Singh TB. Wang ZL. Wang X. Hao WH. Xu JG. Jia JG. Dong B. Zhang XD. Lu NC. Cheng J. Cheng YH. Qu DZ. Zhao FQ. Wang ZM. Feng ZY. Liu HZ. Xu X. Cao ZY. Gu F. Tang XS. Jiang CP. Zheng JL. Bai ZB. Applied Mathematics & Mechanics (English Edition) 1 13 18 26 35 53 58 65 71 79 89 95 100 107 114 Quasi-static and dynamical analysis for viscoelastic timoshenko beam with fractional derivative constitutive relation The tensor denotation of beltrami spherical vortices and their symmetry analysis Time precise integration method for constrained nonlinear control system A family of integrable systems of liouville and lax representation, darboux transformations for its constrained ows Instability and dispersivity of wave propagation in inelastic saturated/unsaturated porous media A form invariance of constrained birkhoÆan system The exact solitary wave solutions for the klein-gordon-schrodinger equations Stability analysis of hopeld neural networks with time delay The extension theorems of cone linear operators Nonlinear saturation of baroclinic instability in the generalized phillips model (i) - the upper bound on the evolution of disturbance to the nonlinearly unstable basic ow The conservation law of nonholonomic system of second-order non-chetave's type in event space Exponential stability of interval dynamical system with multidelay 2t-periodic solution for m order neutral type dierential equations with time delays Computation of supersonic turbulent oweld with transverse injection Preliminary analysis of skating motion 23(1) 2002 Zhu ZY. Li GG. Cheng CJ. Huang YN. Hu X. Deng ZC. Zhong WX. Zhang YF. Zhang HQ. Li XK. Zhang JB. Zhang HW. Chen XW. Luo SK. Mei FX. Xia JN. Han SX. Wang ML. Wang LS. Xu DY. Sheng BH. Liu SY. Mao H. Zhang G. Xiang J. Li DH. Fang JH. Sun JT. Zhang YP. Liu YQ. Deng FQ. Zhang BS. Zhu GH. Sun DC. Hu CB. Cai TM. Hu H. Archive for Rational Mechanics & Analysis 1 27 43 65 The scientic life and inuence of cliord ambrose truesdell iii Stability of spherically symmetric steady states in galactic dynamics against general perturbations Decay of almost periodic solutions of conservation laws Wave interactions in nonlinear elastic strings 161(1) 2002 Ball JM. James RD. Rein G. Frid H. Young R. 7 Archive of Applied Mechanics 1 13 39 52 77 Dynamic fracture behavior of a cracked piezoelectric half space under anti-plane mechanical and in-plane electric impact Complete eigenfunction expansion form of the green's function for elastic layered half-space 3d electroelastic elds in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings Modeling the response of lled elastomers at nite strains by rigid-rod networks Morphological stability of epitaxial thin elastic lms by van der waals force 72(1) 2002 Chen ZT. Worswick MJ. Touhei T. Chen WQ. Lu Y. Ye GR. Cai JB. Drozdov AD. Dorfmann A. Zhao YP. Communications on Pure & Applied Mathematics 395 431 481 509 Riemann-hilbert problem for the small dispersion limit of the kdv equation and linear overdetermined systems of euler-poisson-darboux type Viscosity solutions with shocks The limit behavior of solutions for the cauchy problem of the complex ginzburglandau equation The conformal plate buckling equation 55(4) 2002 Grava T. Giga Y. Wang BX. Chanillo S. Kiessling MKH. Communications on Pure & Applied Mathematics 537 582 633 Vortex dynamics of the full time-dependent ginzburg-landau equations The limit from the schrodinger-poisson to the vlasov-poisson equations with general data in one dimension Convexity and all-time c-innity-regularity of the interface in ame propagation 55(5) 2002 Spirn D. Zhang P. Zheng YX. Mauser NJ. Daskalopoulos P. Lee KA. Communications on Pure & Applied Mathematics 395 431 481 509 Riemann-hilbert problem for the small dispersion limit of the kdv equation and linear overdetermined systems of euler-poisson-darboux type Viscosity solutions with shocks The limit behavior of solutions for the cauchy problem of the complex ginzburglandau equation The conformal plate buckling equation 55(4) 2002 Grava T. Giga Y. Wang BX. Chanillo S. Kiessling MKH. Communications on Pure & Applied Mathematics 537 582 633 654 Vortex dynamics of the full time-dependent ginzburg-landau equations The limit from the schrodinger-poisson to the vlasov-poisson equations with general data in one dimension Convexity and all-time c-innity-regularity of the interface in ame propagation On the well-posedness of the euler equations in the triebel-lizorkin spaces 55(5) 2002 Spirn D. Zhang P. Zheng YX. Mauser NJ. Daskalopoulos P. Lee KA. Chae D. Computer Methods in Applied Mechanics & Engineering 1755 1791 1827 1843 1861 1895 1909 Co-rotational beam elements with warping eects in instability problems Dynamic instability of composite laminated rectangular plates and prismatic plate structures Domain-free discretization method for doubly connected domain and its application to simulate natural convection in eccentric annuli A new locking-free equilibrium mixed element for plane elasticity with continuous displacement interpolation Identication of a constitutive model for the simulation of time-dependent interlaminar debonding processes in composites Discontinuous galerkin methods for incompressible and nearly incompressible elasticity by nitsche's method A combined genetic algorithm and nonlinear least squares method for material characterization using elastic waves 191(17-18) 2002 Battini JM. Pacoste C. Wang S. Dawe DJ. Shu C. Wu YL. Nascimbene R. Venini P. Corigliano A. Mariani S. Hansbo P. Larson MG. Liu GR. Han X. Lam KY. 8 1923 1945 1967 1983 An adaptive procedure based on background cells for meshless methods A stabilized hybrid-stress solid element for geometrically nonlinear homogeneous and laminated shell analyses Lower bound limit analysis by the symmetric galerkin boundary element method and the complex method Numerical simulation of the motion of granular material using object-oriented techniques Liu GR. Tu ZH. Sze KY. Zheng SJ. Zhang XF. Liu YH. Zhao YN. Cen ZZ. Peters B. Dziugys A. Computer Methods in Applied Mechanics & Engineering 2011 2029 2045 2069 2077 2095 2111 2141 2159 2179 2191 Mixed nite element method and high-order local articial boundary conditions for exterior problems of elliptic equation Parametric analysis of frequency of rotating laminated composite cylindrical shells with the wave propagation approach Numerical simulation of delamination growth in curved interfaces Vibration analysis of orthotropic rectangular plates using superelements Structural optimization using equivalent static loads at all time intervals Hierarchical, adaptive, material point method for dynamic energy release rate calculations The construction of free-free exibility matrices for multilevel structural analysis Characterization and design of out-of-ecliptic trajectories using deterministic crowding genetic algorithms Weight minimisation of displacement-constrained truss structures using a strain energy criterion Hysteresis in ow past a naca 0012 airfoil Convergence and accuracy of the path integral approach for elastostatics 191(19-20) 2002 Han HD. Zheng CX. Zhang XM. Munch A. Ousset Y. Ahmadian MT. Zangeneh MS. Choi WS. Park GJ. Tan HL. Nairn JA. Felippa CA. Park KC. Gurl P. Kasdin NJ. Makris PA. Provatidis CG. Mittal S. Saxena P. Pardo E. Computer Methods in Applied Mechanics & Engineering 2223 2235 2261 2283 2297 2317 2337 2371 2403 2427 An improved reissner-mindlin triangular element An automated system for simulation and parameter identication of inelastic constitutive models On a splitting type algorithm for the numerical realization of contact problems with coulomb friction Functionally graded materials for prescribed eld evolution Analysis of thin piezoelectric solids by the boundary element method A posteriori error estimates for a mixed-fem formulation of a non-linear elliptic problem Boundary cloud method: a combined scattered point/boundary integral approach for boundary-only analysis An eÆcient direct bem numerical scheme for phase change problems using fourier series On the solution of an inverse scattering problem in seismic while-drilling technology Reduced bases for model updating in structural dynamics based on constitutive relation error 191(21-22) 2002 Duan HY. Liang GP. Furukawa T. Sugata T. Yoshimura S. Homan M. Haslinger J. Dostal Z. Kucera R. Turteltaub S. Liu YJ. Fan H. Araya R. Barrios TP. Gatica GN. Heuer N. Li G. Aluru NR. Ibanez MT. Power H. Santos JE. Deraemaeker A. Ladeveze P. Leconte P. Computers & Fluids 269 309 335 369 On the combined performance of nonlocal articial boundary conditions with the new generation of advanced multigrid ow solvers Numerical solution of optimal magnetic suppression of natural convection in magneto-hydrodynamic ows by empirical reduction of modes High-resolution hybrid primitive-conservative upwind schemes for the drift ux model An arnoldi approach for generation of reduced-order models for turbomachinery Computers & Fluids 391 393 Special issue - dedicated to professor roger peyret on the occasion of his 65th birthday - preface Special issue - dedicated to professor roger peyret on the occasion of his 65th birthday - foreword 31(3) 2001 Roberts TW. Sidilkover D. Tsynkov SV. Park HM. Jung WS. Fjelde KK. Karlsen KH. Willcox K. Peraire J. White J. 31(4-7) 2002 Bontoux P. Chattot JJ. Hafez M. Haldenwang P. Bontoux P. Chattot JJ. Hafez M. Haldenwang P. 397 421 437 495 509 On a collocation b-spline method for the solution of the navier-stokes equations Multilevel stabilization devices in cfd Numerical modelling of liquid/solid phase transitions - analysis of a gallium melting test Numerical approximation of one-dimensional stationary diusion equations with boundary layers Two adaptive wavelet algorithms for non-linear parabolic partial dierential equations Numerical investigation of the rst bifurcation for the ow in a rotor-stator cavity of radial aspect ratio 10 Dns of wall turbulence: dilute polymers and self-sustaining mechanisms A dual time stepping method for uid-structure interaction problems 539 Computational solution for uid ow under solid/liquid phase change conditions 557 569 Numerical simulation of geophysical turbulence 2d pseudo-spectral parallel navier-stokes simulations of compressible rayleightaylor instability Dynamically adapted mesh renement for combustion front tracking Particles and grid Aspects of unsteady incompressible ow simulations Residual-based compact schemes for multidimensional hyperbolic systems of conservation laws Numerical investigation of meniscus deformation and ow in an isothermal liquid bridge subject to high-frequency vibrations under zero gravity conditions Numerical simulation of separating boundary-layer ow A comparison of second- and sixth-order methods for large-eddy simulations Thirty-six years of shock tting Performances of upwind methods in predicting shear-like ows A spectral projection method for the simulation of complex three-dimensional rotating ows Explicit methods for the solution of the generalized cauchy-riemann equations and simulation of inviscid rotational ows Adaptive and xed segmented domain decomposition multigrid procedures for internal viscous ows Filtering of the pressure spurious modes in p-n-p-n spectral approximations of the stokes system Spectral methods based on nonclassical basis functions: the advection-diusion equation 453 467 481 589 607 627 639 663 683 695 719 725 745 769 787 815 825 Botella O. Canuto C. Cerimele MM. Mansutti D. Pistella F. Cheng WF. Temam R. Chiavassa G. Guichaoua M. Liandrat J. Daube O. Le Quere P. De Angelis E. Casciola CM. Piva R. de Jouette C. Laget O. Le Gouez JM. Viviand H. El Ganaoui M. Lamazouade A. Bontoux P. Morvan D. Ferziger JH. Kose JR. Monismith SG. Fournier E. Gauthier S. Renaud F. Haldenwang P. Pignol D. Huberson SG. Voutsinas SG. Kiris C. Kwak D. Lerat A. Corre C. Lyubimov DV. Lyubimova TP. Skuridin RV. Chen G. Roux B. Marquillie M. Ehrenstein U. Meinke M. Schroder W. Krause E. Rister T. Moretti G. Pandol M. D'Ambrosio D. Raspo I. Hugues S. Serre E. Randriamampianina A. Bontoux P. Roy J. Hafez M. Chattot JJ. Rubin SG. Celestina ML. Srinivasan K. Sabbah C. Forestier MY. Pasquetti R. Shizgal BD. Earthquake Engineering & Structural Dynamics 195 217 445 459 Cyclic analysis and capacity prediction of concrete-lled steel box columns Structural damage detection using the optimal weights of the approximating articial neural networks Closed-form solution for seismic response of adjacent buildings with linear quadratic gaussian controllers Applicability of the h/v spectral ratio of microtremors in assessing site eects on seismic motion Seismic response of rail-counterweight systems in elevators Analytical model of structures with frictional pendulum isolators Extraction of hysteretic properties of seismically isolated bridges from quickrelease eld tests Eect of masonry inlls on seismic performance of a 3-storey r/c frame with non-seismic detailing Application of wavelet theory to identify yielding in seismic response of bi-linear structures Functional series tarma modelling and simulation of earthquake ground motion Experimental and analytical studies on the performance of hybrid isolation systems Performance-based design with semi-active structural control technique Tests on low-ductility rc frames under high- and low-frequency excitations 475 481 Continuous ambient-vibration monitoring of the arch dam of mauvoisin Critical damping of structures with elastically supported visco-elastic dampers 235 261 281 305 333 353 379 399 421 9 31(2) 2002 Susantha KAS. Ge HB. Usami T. Hung SL. Kao CY. Xu YL. Zhang WS. Rodriguez VHS. Midorikawa S. Singh MP. Suarez LE. Rildova. Almazan JL. De la Llera JC. Chen QB. Douglas BM. Maragakis EA. Buckle IG. Lee HS. Woo SW. Pan TC. Lee CL. Fouskitakis GN. Fassois SD. Chang SP. Makris N. Whittaker AS. Thompson ACT. Kurata N. Kobori T. Koshika N. Quek ST. Bian CM. Lu XL. Lu WS. Xiong HB. Darbre GR. Proulx J. Lee Y. Takewaki I. Uetani K. Inoue K. 10 Earthquake Engineering & Structural Dynamics 487 491 515 539 561 583 601 627 653 671 693 719 Special topics issue on performance-based earthquake engineering - foreword Incremental dynamic analysis Inelastic deformation response of sdof systems subjected to earthquakes Evaluation of approximate methods to estimate maximum inelastic displacement demands A modal pushover analysis procedure for estimating seismic demands for buildings An estimation of displacement limits for ductile systems A general framework for risk-consistent seismic design Performance-based seismic engineering: the need for a reliable conceptual comprehensive approach Performance evaluation of new steel frame buildings for seismic loads Generic frame model for simulation of earthquake responses of steel moment frames Earthquake-induced oor horizontal accelerations in buildings A displacement-based approach for the seismic design of continuous concrete bridges 31(3) 2002 Paulay T. Vamvatsikos D. Cornell CA. Riddell R. Garcia JE. Garces E. Miranda E. Ruiz-Garcia J. Chopra AK. Goel RK. Paulay T. Hadjian AH. Bertero RD. Bertero VV. Lee K. Foutch DA. Nakashima M. Ogawa K. Inoue K. Rodriguez ME. Restrepo JI. Carr AJ. Kowalsky MJ. Earthquake Engineering & Structural Dynamics 749 771 791 813 833 851 881 897 921 937 955 977 993 1007 1025 1033 1037 Tuned mass dampers for response control of torsional buildings A mathematical hysteretic model for elastomeric isolation bearings Tangential-projection algorithm for manifold representation in unidentiable model updating problems Investigations into critical earthquake load models within deterministic and probabilistic frameworks Displacement-based seismic analysis for out-of-plane bending of unreinforced masonry walls Risk assessment of an interacting structure-soil system due to liquefaction Fuzzy sliding mode control for a building structure based on genetic algorithms Optimum multiple tuned mass dampers for structures under the ground acceleration based on ddmf and admf Optimal design of passive energy dissipation systems based on h innity and h-2 performances A new modelling strategy for the behaviour of shear walls under dynamic loading Optimal placement of dampers for passive response control Multiple-tuned liquid column dampers for torsional vibration control of structures: experimental investigation Simulations of non-stationary frequency content and its importance to seismic assessment of structures Probabilistic approach for modal identication using non-stationary noisy response measurements only Response spectrum of incompatible acceleration, velocity and displacement histories by praveen k. malhotra, earthquake engng struct. dyn. 2001; 30(2): 279-286 Author's reply to discussion by george mylonakis and costis syngros of 'response spectrum of incompatible acceleration, velocity and displacement histories' earthquake engng struct. dyn. 2001; 30(2): 279-286 Tuned liquid dampers for controlling earthquake response of structures by p. banerji et al., earthquake engng struct. dyn. 2000;29(5): 587-602 Engineering Structures 385 397 419 429 443 455 469 479 491 Frp-strengthened rc beams. i: review of debonding strength models Frp-strengthened rc beams. ii: assessment of debonding strength models Experimental tests on reinforced concrete columns under biaxial quasi-static loading Mechanical properties of structural bamboo for bamboo scaoldings Seismic retrot of exible steel frames using thin inll panels Cracking analysis of rc members using polynomial strain distribution function Experimental studies on shear lag of box girders Numerical analysis of dynamic stability under random excitation Green's functions for 2.5d elastodynamic problems in a free solid layer formation 31(4) 2002 Singh MP. Singh S. Moreschi LM. Hwang JS. Wu JD. Pan TC. Yang G. Katafygiotis LS. Lam HF. Abbas AM. Manohar CS. Doherty K. GriÆth MC. Lam N. Wilson J. Koutsourelakis S. Prevost JH. Deodatis G. Wang AP. Lee CD. Li CX. Yang JN. Lin S. Kim JH. Agrawal AK. Mazars J. Kotronis P. Davenne L. Singh MP. Moreschi LM. Shum KM. Xu YL. Wang JJ. Fan LC. Qian S. Zhou J. Yuen KV. Beck JL. Katafygiotis LS. Mylonakis G. Syngros C. Malhotra PK. Yalla SK. Kareem A. 24(4) 2002 Smith ST. Teng JG. Smith ST. Teng JG. Qiu FW. Li WF. Pan P. Qian JR. Chung KF. Yu WK. Bruneau M. Bhagwagar T. Kwak HG. Song JY. Luo QZ. Wu YM. Tang J. Li QS. Williamson EB. Rungamornrat J. Tadeu A. Antonio J. 501 517 Damage assessment in reinforced concrete beams using eigenfrequencies and mode shape derivatives Seismic response control of large-span machinery building on top of ship lift towers using er/mr moment controllers Ndambi JM. Vantomme J. Harri K. Qu WL. Xu YL. Lv MY. European Journal of Mechanics A-Solids 1 13 49 61 73 85 105 121 133 151 167 A comparison between the perzyna viscoplastic model and the consistency viscoplastic model Boundary layers in thin elastic shells with developable middle surface A variational inequality-based formulation of the frictional contact law with a non-associated sliding rule Strength or toughness? a criterion for crack onset at a notch A shrink-t shaft subject to torsion Thermodynamics and continuum fracture mechanics for nonlocal-elastic plastic materials Dynamic fragmentation of brittle solids: a multi-scale model Uniaxial compressive failure of brittle materials as instability of damaging microcracked solids Novel viscoelastic models for elastomers under nite strains Instability analysis of vibrations of a uniformly moving mass in one and twodimensional elastic systems Dynamic modelling of the double wishbone motor-vehicle suspension system 21(1) 2002 Heeres OM. Suiker ASJ. de Borst R. Karamian P. Sanchez-Hubert J. Hjiaj M. de Saxce G. Mroz Z. Leguillon D. Sackeld A. Barber JR. Hills DA. Truman CE. Polizzotto C. Denoual C. Hild F. Gambarotta L. Monetto E. Dimitrienko YI. Kononov AV. de Borst R. Attia HA. Experimental Mechanics 1 Flexural fatigue behavior of threaded connections for large diameter pipes 8 A tension split hopkinson bar for investigating the dynamic behavior of sheet metals Application of the fourier transform in electronic speckle photography Multiple force identication for complex structures Circumferential strain measurement for a concrete cylinder in uniaxial compression by a ber optic sensor The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity A new microtensile tester for the study of mems materials with the aid of atomic force microscopy A shear-compression specimen for large strain testing High-strain-rate compressive behavior of a rigid polyurethane foam with various densities A parametric study of laser induced thin lm spallation Fabric thickness dynamic measurement during a classic uniaxial tensile test Pulse shaping techniques for testing brittle materials with a split hopkinson pressure bar Heating during shearing and opening dominated dynamic fracture of polymers Novel load cell for measuring axial force, shear force, and bending movement in large-scale structural experiments In-situ tensile testing of nano-scale specimens in sem and tem 18 25 37 43 51 58 65 74 84 93 107 115 123 Experiments in Fluids 1 3 37 44 55 Retirement of wolfgang merzkirch Velocity prole characterization in sub-millimeter diameter tubes using molecular tagging velocimetry Plane jets impinging on porous walls Forces, moment and wave pattern for surface combatant in regular head waves part ii. measurement results and discussion Multiple hot-lm sensor array calibration and skin friction measurement Control of backward-facing step ow using a apping foil Accurate measurement of hydrodynamic interactions between a particle and walls 66 Experimental study of the synthesis of fused silica by direct combustion hydrolysis 16 27 11 42(1) 2002 Varma AH. Salecha AK. Wallace B. Russell BW. Huh H. Kang WJ. Han SS. Zhang YP. Zhu HN. Zhou WL. Liu HF. Adams R. Doyle JF. Li QB. Ansari F. Tomlinson RA. Patterson EA. Chasiotis I. Knauss WG. Rittel D. Lee S. Ravichandran G. Chen W. Lu F. Winfree N. Wang JL. Weaver RL. Sottos NR. Fontaine S. Durand B. Freyburger JM. Frew DJ. Forrestal MJ. Chen W. Bjerke T. Lambros J. Blakeborough A. Clement D. Williams MS. Woodward N. Haque MA. Saif MTA. 32(1) 2002 Gharib M. Rockwell D. Taylor A. Maynes D. Webb AR. Cant R. Castro I. Walklate P. Gui L. Longo J. Metcalf B. Shao J. Stern F. Desgeorges O. Lee T. Kafyeke F. Lai JCS. Yue J. Platzer MF. Masmoudi K. Lecoq N. Anthore R. Bostel F. Feuillebois F. Linow S. Schneider C. Geiss S. Janicka J. Hassel EP. Rudiger F. 12 76 87 99 106 116 121 136 Coherent structure identication from wavelet analysis of particle image velocimetry data A kilohertz frame rate cinemagraphic piv system for laboratory-scale turbulent and unsteady ows Eects of gurney aps on the lift enhancement of a cropped nonslender delta wing Performance of digital image velocimetry processing techniques A three-dimensional photographic method for measurement of phase distribution in dilute bubble ow Voronoi imaging methods for the measurement of granular ows Further characterization of large-scale coherent structure signatures in a turbulent-plane mixing layer Camussi R. Upatnieks A. Laberteaux K. Ceccio SL. Li YC. Wang JJ. Tan GK. Zhang PF. McKenna SP. McGillis WR. Luo R. Song Q. Yang XY. Wang Z. Capart H. Young DL. Zech Y. Auburn S. Boisson HC. Bonnet JP. Fatigue & Fracture of Engineering Materials & Structures 99 Fatigue life recovery in aluminium alloy aircraft structure 111 127 141 Initiation and early growth of fatigue cracks in an aerospace aluminium alloy Closure of plane-strain cracks under large-scale yielding conditions In situ investigation of small fatigue crack growth in poly-crystal and singlecrystal aluminium alloys Shape optimization of critical stiener runouts for f-111 airframe life extension 151 173 187 201 215 223 231 Adhesively bonded joints under cyclic loading spectra Self-similar crack patterns induced by spatial stress uctuations Plastically elastically dominant fatigue interaction in 316l stainless steel and 6061t6 aluminium alloy Features of fatigue crack growth due to repeated thermal shock The eect of solution heat-treatment time on the fatigue properties of an al-si-mg casting alloy A perturbation solution for a crack in a power-law material under gross yielding 25(2) 2002 Sharp PK. Liu Q. Barter SA. Baburamani P. Clark G. Barter SA. Sharp PK. Holden G. Clark G. Wang CH. Rose LRF. Newman JC. Zhang XP. Wang CH. Ye L. Mai YW. Heller M. McDonald M. Burchill M. Watters KC. Jones R. Kotousov A. Marshall IH. Dyskin AV. Wong YK. Hu XZ. Norton MP. Kerezsi BB. Price JWH. Kotousov AG. Davidson CJ. GriÆths JR. Machin AS. Chen GX. Wang CH. Rose LRF. Flow, Turbulence & Combustion 81 107 125 137 143 Using a fuzzy piecewise regression analysis to predict the nonlinear time-series of turbulent ows with automatic change-point detection Particle/turbulence interactions, mass transfer and gas/solid chemistry in a cfbc riser Extended proper orthogonal decomposition: application to jet/vortex interaction Analysis of streamwise velocity uctuations in turbulent pipe ow with the use of an ultrasonic doppler owmeter On modelling periodic motion with turbulence closures 67(2) 2001 Tseng YH. Durbin P. Tzeng GH. Zevenhoven R. Jarvinen M. Maurel S. Boree J. Lumley JL. Alfonsi G. Cotton MA. Craft TJ. Guy AW. Launder BE. IMA Journal of Applied Mathematics 1 23 On the far-eld operator in elastic obstacle scattering Mathematical analysis of the optimal location of wastewater outfalls 41 Mathematical modelling for keyhole surgery simulations: a biomechanical model for spleen tissue Asymptotic simplication for a reaction-diusion problem with a nonlinear boundary condition 69 67(1) 2002 Alves CJS. Kress R. Alvarez-Vazquez LJ. Martinez A. Rodriguez C. Vazquez-Mendez ME. Davies PJ. Carter FJ. Cuschieri A. de Pablo A. Quiros F. Rossi JD. International Journal for Numerical & Analytical Methods in Geomechanics 99 121 139 163 181 Computational mechanics of the steel-concrete interface A visco-plastic constitutive model for granular soils modied according to nonlocal and gradient approaches Numerical solution for consolidation and desiccation of soft soils EÆcient conditional modeling for geotechnical uncertainty evaluation Upper bound limit analysis using linear nite elements and non-linear programming 26(2) 2002 Ben Romdhane MR. Ulm FJ. di Prisco C. Imposimato S. Aifantis EC. Yao DTC. de Oliveira WL. Cai XC. Znidarcic D. Graettinger AJ. Lee J. Reeves HW. Lyamin AV. Sloan SW. 13 International Journal for Numerical & Analytical Methods in Geomechanics 217 231 259 273 299 Three-dimensional nite element analysis of the interaction between tunneling and pile foundations Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium Integration and calibration of a plasticity model for granular materials Image-based modelling and analysis of microstructures for two-scale problems in geomechanics Fundamental solutions for a uid-saturated, transversely isotropic, poroelastic solid Mroueh H. Shahrour I. Giraud A. Homand F. Labiouse V. Jacobsson L. Runesson K. Terada K. Kyoya T. Kazama M. Lee K. Oyang L. Taguchi I. Kurashige M. International Journal for Numerical Methods in Engineering 1259 1277 1301 1323 1337 1353 1377 1393 1415 1433 1461 1477 1491 Computational micro-mechanical model of exible woven fabric for nite element impact simulation An interactive geometry utility environment for multi-disciplinary computational engineering Adaptive backward euler time stepping with truncation error control for numerical modelling of unsaturated uid ow Convergence analysis of a hierarchical enrichment of dirichlet boundary conditions in a mesh-free method Tetrahedral composite nite elements Higher-order responses of three-dimensional elastic plate structures and their numerical illustration by p-fem Tetrahedral mesh improvement via optimization of the element condition number An energy and momentum conserving method for rigid-exible body dynamics A ux-limited numerical method for solving the mhd equations to simulate propulsive plasma ows Multifrontal incomplete factorization for indenite and complex symmetric systems Three-dimensional nite element calculations in acoustic scattering using arbitrarily shaped convex articial boundaries On non-linear behaviour of spherical shallow shells bonded with piezoelectric actuators by the dierential quadrature element method (dqem) A canonical form return mapping algorithm for rate independent plasticity 1533 1557 1575 1593 1615 1629 1641 1675 1695 1721 1751 An adaptive-recursive staggering strategy for simulating multield coupled processes in microheterogeneous solids Thermo-elasto-plastic nite element analysis of quasi-state processes in eulerian reference frames On congurational forces in the context of the nite element method Hat interpolation wavelet-based multi-scale galerkin method for thin-walled box beam analysis A new numerical method for the boundary optimal control problems of the heat conduction equation Comparison of method of lines and nite dierence solutions of 2-d navier-stokes equations for transient laminar pipe ow Stress analysis of gear teeth using displacement potential function and nite differences A ga-based technique for layout optimization of truss with stress and displacement constraints A one-dimensional theory of thin-walled curved rectangular box beams under torsion and out-of-plane bending Analytical integrations in 2d bem elasticity Development of shear locking-free shell elements using an enhanced assumed strain formulation Non-singular boundary integral formulations for plane interior potential problems 53(6) 2002 Tabiei A. Ivanov I. Zheng Y. Weatherill NP. Turner-Smith EA. Kavetski D. Binning P. Sloan SW. Han WM. Wagner GJ. Liu WK. Thoutireddy P. Molinari JF. Repetto EA. Ortiz M. Dauge M. Rossle A. Yosibash Z. Freitag LA. Knupp PM. Puso MA. Sankaran K. Martinelli L. Jardin SC. Choueiri EY. Qu Y. Fish J. Tezaur R. Macedo A. Farhat C. Djellouli R. Wang XW. Wang YL. Keavey MA. International Journal for Numerical Methods in Engineering 1511 26(3) 2002 53(7) 2002 Zohdi TI. Shanghvi JY. Michaleris P. Mueller R. Kolling S. Gross D. Kim YY. Jang GW. Park HM. Lee WJ. Selcuk N. Tarhan T. Tanrikulu S. Akanda MAS. Ahmed SR. Uddin MW. Azid IA. Kwan ASK. Seetharamu KN. Kim YY. Kim Y. Salvadori A. de Sa JMAC. Jorge RMN. Valente RAF. Areias PMA. Hwang WS. Hung LP. Ko CH. 14 International Journal for Numerical Methods in Engineering 1765 1781 1801 1831 A nite point method for compressible ow A new class of c-n interpolations and its application to the nite element method Time-discretized variational formulation of non-smooth frictional contact Arbitrary lagrangian-eulerian (ale) formulation for hyperelastoplasticity 1853 1871 An implicit bem formulation for gradient plasticity and localization phenomena Hierarchical model adaptivity in nite element analysis for non-linear plate problems Finite element evaluation of mixed mode stress intensity factors in functionally graded materials Moving particle nite element method The extended nite element method (xfem) for solidication problems Design space optimization using a numerical design continuation method Three-dimensional nite element solution of gas-assisted injection moulding 1903 1937 1959 1979 2003 53(8) 2002 Lohner R. Sacco C. Onate E. Idelsohn S. Hashemolhosseini H. Sadati N. Farzin M. Pandol A. Kane C. Marsden JE. Ortiz M. Rodriguez-Ferran A. Perez-Foguet A. Huerta A. Benallal A. Fudoli CA. Venturini WS. Fu K. Kim JH. Paulino GH. Hao S. Park HS. Liu WK. Chessa J. Smolinski P. Belytschko T. Kim YI. Kwak BM. Ilinca F. Hetu JF. International Journal for Numerical Methods in Engineering 2019 2043 2061 2087 2117 2143 2163 2185 2201 2217 2239 2253 Contact between 3d beams with rectangular cross-sections Second-order optimal control algorithm for complex systems Mixed-enhanced formulation for geometrically linear axisymmetric problems Meshfree analysis and design sensitivity analysis for shell structures A simple algorithm for localized construction of non-matching structural interfaces Low-frequency assessment of the in situ acoustic absorption of materials in rooms: an inverse problem approach using evolutionary optimization A stream function implicit nite dierence scheme for 2d incompressible ows of newtonian uids Hybrid time domain solvers for the maxwell equations in 2d Development of a simple and eÆcient method for robust optimization Implementation of cyclic plasticity models based on a general form of kinematic hardening Studies of multi-start clustering for global optimization An approach to multi-start clustering for global optimization with non-linear constraints Litewka P. Wriggers P. Kaplan ML. Heegaard JH. Kasper EP. Taylor RL. Kim NH. Choi KK. Chen JS. Botkin ME. Park KC. Felippa CA. Rebel G. Dutilleux G. Sgard FC. Kristiansen UR. Bubnovich VI. Rosas CE. Moraga NO. Abenius E. Andersson U. Edelvik F. Eriksson L. Ledfelt G. Jung DH. Lee BC. Kobayashi M. Ohno N. Tu W. Mayne RW. Tu W. Mayne RW. International Journal for Numerical Methods in Engineering 2271 2305 2311 2329 2357 2389 2413 Conservation properties of a time fe method - part iii: mechanical systems with holonomic constraints Speeding up the solution of thermal ehl problems A simplied approach for incorporating thickness stress in the analysis of sheet metal forming using shell elements A posteriori error estimation in non-linear fe analyses of shell structures Constitutive modeling of cementitious materials in the framework of chemoplasticity An optimal high-order non-reecting nite element scheme for wave scattering problems Singularities in anisotropic steady-state heat conduction using a boundary element method 2445 2463 Optimum design of stochastically excited non-linear dynamic systems without geometric constraints A plasticity based model and an adaptive algorithm for nite element analysis of reinforced concrete panels Remeshing for metal forming simulations - part 1: two-dimensional quadrilateral remeshing 53(10) 2002 Betsch P. Steinmann P. Ford JM. Chen K. Cho JW. Yang DY. Chung WJ. Lackner R. Mang HA. Lackner R. Hellmich C. Mang HA. Givoli D. Patlashenko I. Mera NS. Elliott L. Ingham DB. Lesnic D. International Journal for Numerical Methods in Engineering 2429 53(9) 2002 53(11) 2002 Oblak MM. Lesnika AS. Butinar BJ. Pravida J. Wunderlich W. Kwak DY. Cheon JS. Im YT. 2501 2529 2549 2569 Remeshing for metal forming simulations - part ii: three-dimensional hexahedral mesh generation A 3d brick element based on hu-washizu variational principle for mesh distortion Non-planar 3d crack growth by the extended nite element and level sets - part i: mechanical model Non-planar 3d crack growth by the extended nite element and level sets - part ii: level set update Cao YP. Hu N. Lu J. Fukunaga H. Yao ZH. Moes N. Gravouil A. Belytschko T. Gravouil A. Moes N. Belytschko T. International Journal for Numerical Methods in Engineering 2587 2617 2643 2673 2701 2721 Non-linear version of stabilized conforming nodal integration for galerkin meshfree methods Hybrid-stress solid elements for shell structures based upon a modied variational functional A control volume capacitance method for solidication modelling with mass transport Automatic generation of anisotropic quadrilateral meshes on three-dimensional surfaces using metric specications Implicit stress integration procedure for small and large strains of the gurson material model Reconstructing dynamic events from time-limited spatially distributed data 447 471 Gas-assisted uid displacement in a circular tube and a rectangular channel EÆcient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder Identication of regions of fastest mixing in a system of point vortices Stability of explicit advection schemes. the balance point location rule Sze KY. Lo SH. Davey K. Rodriguez NJ. Lee YK. Lee CK. Kojic M. Vlastelica I. Zivkovic M. Doyle JF. 38(5) 2002 Kamisli F. Ryan ME. Shu C. Zhu YD. Ramachandran P. Rajan SC. Leonard BP. International Journal for Numerical Methods in Fluids 515 533 555 567 589 A reappraisal of taylor-galerkin algorithm for drying-wetting areas in shallow water computations Numerical solution of the ow of thin viscous sheets under gravity and the inverse windscreen sagging problem Three dimensional tide-induced circulation model on a triangular mesh An unconditionally stable, explicit godunov scheme for systems of conservation laws A simple and eÆcient error analysis for multi-step solution of the navier-stokes equations 38(6) 2002 Quecedo M. Pastor M. Hunt R. Jiang WS. Sun WX. Guinot V. Fithen RM. International Journal for Numerical Methods in Fluids 609 625 647 677 Application of local grid renement to vortex motion due to a solitary wave passing over a submerged body Improved linear interpolation practice for nite-volume schemes on complex grids Iterative explicit simulation of 1d surges and dam-break ows Simulation of pressure-tooling wire-coating ow with phan-thien/tanner models International Journal for Numerical Methods in Fluids 711 729 747 769 789 A three-dimensional boundary layer scheme: stability and accuracy analyses Selection of a staggered grid for inertia-gravity waves in shallow water Finite volume scheme for the solution of uid ow problems on unstructured non-staggered grids Numerical solutions of the shallow water equations with discontinuous bed topography Numerical solution of incompressible ows by discrete singular convolution 53(12) 2002 Chen JS. Yoon SP. Wu CT. International Journal for Numerical Methods in Fluids 407 429 15 Kwak DY. Im YT. 38(7) 2002 Tang CJ. Chang JH. Lehnhauser T. Schafer M. Hsu CT. Yeh KC. Ngamaramvaranggul V. Webster MF. 38(8) 2002 Horri-Naceur J. Buisine D. Beckers JM. Barton IE. Markham-Smith D. Bresslo N. Zhou JG. Causon DM. Ingram DM. Mingham CG. Wan DC. Zhou YC. Wei GW. 16 International Journal for Numerical Methods in Fluids 811 849 861 881 895 A low-dimensional spectral approach for the nonlinear overstability of purely elastic uids Parallel solution of a coupled ow and transport model for shallow water A low-dimensional spectral approach for transient axisymmetric free-surface ow inside thin cavities of arbitrary shape On the use of the galerkin method for 3d numerical modelling of the general circulation: the south atlantic experiment The eect of solutal undercooling on double-diusive convection and macrosegregation during binary alloy solidication: a numerical investigation 38(9) 2002 Khayat RE. Sommeijer BP. van der Houwen PJ. Khayat RE. Simanowski A. Harari J. Giarolla E. Chakraborty S. Dutta P. International Journal of Engineering Science 347 367 385 401 411 433 449 461 Stress analysis of a bonded repair over a corrosion grind-out using an inclusion model with a second ordered eigenstrain theory Stochastic equations of rigid-thermo-viscoplasticity in metal forming process Growth and decay in generalized thermoelasticity Contact problem for porous elastic strip Unsteady ow and heat transfer of a viscous uid in the stagnation region of a three-dimensional body with a magnetic eld Fourth-order techniques for identifying a control parameter in the parabolic equations Rayleigh-benard convection in a micropolar ferromagnetic uid Description of magneto rheological behavior with internal variables 40(4) 2002 Duong CN. Yu J. Grzywinski M. Sluzalec A. Payne LE. Song JC. Scalia A. Kumari M. Nath G. Dehghan M. Abraham A. Chen KC. Yeh CS. International Journal of Engineering Science 485 499 511 531 549 569 587 On the spatial behaviour of the transient and steady-state solutions in thin plates with transverse shear deformation A method to model simple tension experiments using nite elasticity theory with an application to some polyurethane foams A poroelastic bone model for internal remodeling Non-similarity solution and correlation of transient heat transfer in laminar boundary layer ow over a wedge On the micromorphic thermoelasticity Evaluation of the stress eld around a notch tip using contour integrals A two-dimensional problem for a half-space in magneto-thermoelasticity with thermal relaxation 40(5) 2002 Ciarletta M. Murphy JG. Rogerson GA. Papathanasopoulou VA. Fotiadis DI. Foutsitzi G. Massalas CV. Cheng WT. Lin HT. Iesan D. Chang JH. Kang LK. Sherief HH. Helmy KA. International Journal of Fracture 107 125 153 175 Finite volume analysis of dynamic fracture phenomena - i. a node release methodology Finite volume analysis of dynamic fracture phenomena - ii. a cohesive zone type methodology Crack-tip constraint in mode ii deformation Prediction of shear crack growth direction under compressive loading and plane strain conditions 113(2) 2002 Stylianou V. Ivankovic A. Stylianou V. Ivankovic A. Ayatollahi MR. Smith DJ. Pavier MJ. Isaksson P. Stahle P. International Journal of Fracture 195 213 233 253 267 285 Eects of mode mix upon fracture behavior of a solder joint Afm and sem observation on mechanism of fatigue crack growth in an fe-si single crystal Thin layer splitting along the elastic-plastic solid surface Fractal characteristics of composite pipes defects in torsion testing Dual boundary element method for axisymmetric crack analysis Determination of stress intensity factors for bimaterial interface stationary rigid line inclusions by boundary element method 113(3) 2002 Kang KJ. Kim DH. Choi SH. Oda Y. Furuya Y. Noguchi H. Higashida K. Wei YG. Cetera A. Blazejewski W. de Lacerda LA. Wrobel LC. Lee KY. Kwak SG. 17 International Journal of Fracture 295 309 327 345 367 A new look at energy release rate in fracture mechanics Crack-tip elds in anisotropic shells The fracture behaviour of intermetallic tial alloys with and without warm prestressing Report on onr workshop on fracture scaling Viscoelastic crack growth process in wood timbers: an approach by the nite element method for mode i fracture 113(4) 2002 Sun CT. Wang CY. Yuan FG. Yang S. Chen JH. Pippan R. Hebesberger T. Kolednik O. Bazant ZP. Rajapakse YDS. Allen DH. Ballarini R. Espinosa HD. Gao H. Gettu R. Jirasek M. Pijaudier-Cabot G. Planas J. Ulm FJ. Dubois F. Chazal C. Petit C. International Journal of Heat & Fluid Flow 107 109 137 Preface Heat transfer research on gas turbine airfoils at nasa grc Elevated freestream turbulence eects on heat transfer for a gas turbine vane 148 Progress in the generalization of wall-function treatments 161 Scalar dispersion from an instantaneous line source at the wall of a turbulent channel for medium and high prandtl number uids Turbulent heat transfer from a multi-layered wall-mounted cube matrix: a large eddy simulation Heat transfer in transitional and turbulent boundary layers with system rotation Heat transfer enhancement by gortler instability Investigation of the ow eld of a highly heated jet of air 173 186 194 205 23(2) 2002 Ball KS. Schmidt FW. Garg VK. Thole KA. Radomsky RW. Kang MB. Kohli A. Craft TJ. Gerasimov AV. Iacovides H. Launder BE. Papavassiliou DV. Niceno B. Dronkers ADT. Hanjalic K. Yamawaki D. Obi S. Masuda S. Toe R. Ajakh A. Peerhossaini H. Anderson SM. Bremhorst K. International Journal of Heat & Mass Transfer 1789 Congratulations to prof. erich hahne, on the occasion of his 70th birthday 1791 Subcooled ow boiling heat transfer of r-134a and the associated bubble characteristics in a vertical plate heat exchanger Second law analysis of a waste heat recovery steam generator Convective heat transfer of exothermic reactive gas owing across a heating cylinder coated with platinum catalyst in a narrow duct Flow and heat transfer in rotating two-pass rectangular channels (ar=2) by reynolds stress turbulence model Measurement of apparent solid-side mass diusivity of a water vapor-silica gel system Computational modeling for honeycomb-stator gas annular seal Temperature solution in multi-dimensional multi-layer bodies Eects of radius and heat transfer on the prole of evaporating thin liquid lm and meniscus in capillary tubes Energy analysis of evaporating thin falling lm instability in vertical tube Analytical solutions of 1-d heat conduction problem for a single n with temperature dependent heat transfer coeÆcient - i. closed-form inverse solution Analytical solutions of the 1-d heat conduction problem for a single n with temperature dependent heat transfer coeÆcient - ii. recurrent direct solution 1807 1815 1823 1839 1849 1865 1879 1889 1895 1905 45(9) 2002 Muller-Steinhagen H. Minkowycz WJ. Hartnett JP. Rose JW. Hsieh YY. Chiang LJ. Lin TF. Reddy BV. Ramkiran G. Kumar KA. Nag PK. Itaya Y. Hiroi T. Matsuda H. Hasatani M. Al-Qahtani M. Jang YJ. Chen HC. Han JC. Ni CC. San JY. Chochua G. Shyy W. Moore J. Haji-Sheikh A. Beck JV. Qu W. Ma TZ. Miao JY. Wang JL. Du XZ. Wang BX. Wu SR. Jiang SY. Dul'kin IN. Garas'ko GI. Dul'kin IN. Garas'ko GI. International Journal of Plasticity 281 313 345 359 Reactive plasticity for clays during dehydration and rehydration. part 1: concepts and options A non-linear analysis of non-isothermal wave propagation in linear-elastic uidsaturated porous media Steady crack growth in elastic-plastic uid-saturated porous media Comparison of two grain interaction models for polycrystal plasticity and deformation texture prediction 18(3) 2002 Hueckel T. Gajo A. Radi E. Bigoni D. Loret B. Van Houtte P. Delannay L. Kalidindi SR. 18 379 399 415 Energy balance and identication of hardening moduli in plastic deformation processes Application of a large deformation model to unstable tensile stretching of polyethylene Damage and size eect during superplastic deformation Mroz Z. Oliferuk W. Sweeney J. Collins TLD. Coates PD. Unwin AP. Duckett RA. Ward IM. Taylor MB. Zbib HM. Khaleel MA. Inverse Problems in Engineering 431 Electrical process tomography with known internal structures and resistivities 455 Local spline-approximation method of solving some coeÆcient inverse problems for dierential equation of the parabolic type Numerical solution of a rst kind integral equation of potential theory Developing nuclear magnetic resonance imaging for engineering applications Estimation of thermophysical properties of composites using multi-parameter estimation and zeroth-order regularization Multi-dimensional heat ux reconstruction using narrow-band thermochromic liquid crystal thermography State space models in process tomography - approximation of state noise covariance 471 487 507 537 561 9(5) 2001 Heikkinen LM. Vauhkonen M. Savolainen T. Leinonen K. Kaipio JP. Grebennikov A. Flores JD. Watson AT. Hollenshead JT. Chang CTP. Aviles-Ramos C. Haji-Sheikh A. Kassab AJ. Divo E. Kapat JS. Seppanen A. Vauhkonen M. Somersalo E. Kaipio JP. Inverse Problems in Engineering 587 619 645 671 Absorption coeÆcient estimation in heterogeneous media using a domain partition consistent with divergent beams Boundary inverse heat conduction problem: algorithm and error analysis Parametric identication of viscoelastic materials from time and frequency domain data Stochastic regularization of feedwater ow rate evaluation for the venturi meter fouling problem in nuclear power plants 9(6) 2001 Montero RFC. Roberty NC. Neto AJS. Alifanov OM. Nenarokomov AV. Mossberg M. Hillstrom L. Abrahamsson L. Gribok AV. Attieh IK. Hines JW. Uhrig RE. Journal of Composite Materials 3 19 47 69 93 Nonlinear viscoelastic nite element analyses of thermosetting polymeric composites during cool-down after curing Cure cycle for thick glass/epoxy composite laminates The response of composite joints with bolt-clamping loads, part 1: model development The response of composite joints with bolt-clamping loads, part ii: model verication Stress and failure analysis of 3d angle interlock woven composites 36(1) 2002 Yi S. Chian KS. Hilton HH. Oh JH. Lee DG. Sun HT. Chang FK. Qing XL. Sun HT. Chang FK. Qing XL. Naik NK. Azad SNM. Prasad PD. Journal of Computational Physics 363 398 412 438 454 487 525 559 576 584 604 645 674 702 Separable and nonseparable multiwavelets in multiple dimensions Evaluation of the modied bessel function of the third kind of imaginary orders Bounded skew high-order resolution schemes for the discrete ordinates method Algebraic splitting for incompressible navier-stokes equations High-order monotonicity-preserving compact schemes for linear scalar advection on 2-d irregular meshes On time-splitting spectral approximations for the schrodinger equation in the semiclassical regime Flux correction tools for nite elements Semi-lagrangian schemes for hamilton-jacobi equations, discrete representation formulae and godunov methods Calculation of the quantum entanglement measure of bipartite states, based on relative entropy, using genetic algorithms Construction of commutative lters for les on unstructured meshes Motion of curves constrained on surfaces using a level-set approach Hyperbolic divergence cleaning for the mhd equations Hybrid ux-splitting schemes for a two-phase ow model A comparison of spectral and vortex methods in three-dimensional incompressible ows 175(2) 2002 Tymczak CJ. Niklasson AMN. Roder H. Gil A. Segura J. Temme NM. Coelho PJ. Henriksen MO. Holmen J. Tran QH. Scheurer B. Bao WZ. Jin S. Markowich PA. Kuzmin D. Turek S. Falcone M. Ferretti R. Ramos RV. Souza RF. Marsden AL. Vasilyev OV. Moin P. Cheng LT. Burchard P. Merriman B. Osher S. Dedner A. Kemm F. Kroner D. Munz CD. Schnitzer T. Wesenberg M. Evje S. Fjelde KK. Cottet GH. Michaux B. Ossia S. VanderLinden G. 713 739 764 792 Numerical simulation of isotropic turbulence using a collocated approach and a nonorthogonal grid system An explicit fourth-order orthogonal curvilinear staggered-grid fdtd method for maxwell's equations Accuracy and conservation properties of a three-dimensional unstructured staggered mesh scheme for uid dynamics Exactly conservative semi-lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique (vol 174, pg 171, 2001) Xie ZQ. Chan CH. Zhang B. Zhang X. Schmidt D. Perot B. Nakamura T. Tanaka R. Yabe T. Takizawa K. Journal of Computational Physics 1 20 40 70 93 129 145 170 196 205 EÆcient and rapid numerical evaluation of the two-electron, four-center coulomb integrals using nonlinear transformations and useful properties of sine and bessel functions A nonlinear ux split method for hyperbolic conservation laws Grid adaptation for functional outputs: application to two-dimensional inviscid ows 2d simulation of a silicon mesfet with a nonparabolic hydrodynamical model based on the maximum entropy principle Reference jacobian optimization-based rezone strategies for arbitrary lagrangian eulerian methods Numerical analysis of dusty-gas ows C-innity-interpolation of discrete elds on regular and irregular grids A numerical method for the solution of electromagnetic wave diraction problems on perfectly conducting screens Optimal annealing schedules for a modied tsallis statistics A second-order-accurate symmetric discretization of the poisson equation on irregular domains 176(1) 2002 Safouhi H. Stiriba Y. Venditti DA. Darmofal DL. Romano V. Knupp P. Margolin LG. Shashkov M. Saito T. Giona M. Cerbelli S. Kanaun SK. Franz A. Homann KH. Gibou F. Fedkiw RP. Cheng LT. Kang MJ. Journal of Computational Physics 231 276 295 330 345 363 384 402 430 456 483 A cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions Dust dynamics in protoplanetary disks: parallel computing with pvm Numerical study of quantum resonances in chaotic scattering Consistent boundary conditions for multicomponent real gas mixtures based on characteristic waves A stable scheme for the numerical computation of long wave propagation in temporal laminates A pressure-based method for turbulent cavitating ow computations An eÆcient spectral-projection method for the navier-stokes equations in cylindrical geometries ii. three-dimensional cases A numerical method to simulate radio-frequency plasma discharges Exponential time dierencing for sti systems Stress calculations on multiply connected domains A parallelized meshfree method with boundary enrichment for large-scale cfd 176(2) 2002 Calhoun D. Marcos CD. Barge P. Marcos RD. Lin KK. Okong'o N. Bellan J. Weekes SL. Senocak I. Shyy W. Lopez JM. Marques F. Shen J. Hammond EP. Mahesh K. Moin P. Cox SM. Matthews PC. Helsing J. Jonsson A. Zhang LT. Wagner GJ. Liu WK. Journal of Elasticity 87 113 137 153 Exponential stability to a contact problem of partially viscoelastic materials A partially built-in plate under uniform load A boussinesq-cerruti solution set for constant and linear distribution of normal and tangential load over a triangular area An exact theory for circular, end-loaded, anisotropic beams of narrow rectangular cross section 63(2) 2001 Rivera JEM. Oquendo HP. Gregory RD. Li JS. Berger EJ. Ladeveze P. Simmonds JG. Journal of Elasticity 171 221 Asymptotic analysis of the eversion of nonlinearly elastic shells - ii. incompressible shells Implications and constraints of time-independent poisson ratios in linear isotropic and anisotropic viscoelasticity 19 Lopes AS. Palma JMLM. 63(3) 2001 Antman SS. Srubshchik LS. Hilton HH. 20 Journal of Engineering Mathematics 1 23 45 65 A numerical study of pulsatile blood ow in an eccentric catheterized artery using a fast algorithm Boundary-layer behaviour in a hydraulic theory of horizontal oil wells Mass-transport enhancement in regions bounded by rigid walls Acoustically generated unsteady vorticity eld in a long narrow cylinder with sidewall injection 42(1) 2002 Daripa P. Dash RK. Schulkes RMSM. King AC. Trevelyan PMJ. Kalliadasis S. Merkin JH. Scott SK. Kirkkopru K. Kassoy DR. Zha Q. Staab PL. Journal of Engineering Mechanics-ASCE 134 143 156 164 172 184 190 202 209 220 231 240 249 Response of 1/4-scale concrete masonry unit (cmu) walls to blast Plane turbulent wall jets in shallow tailwater Study of the behavior of concrete under triaxial compression Wave diraction by a vertical cylinder with a porous ring plate Use of microwaves for damage detection of ber reinforced polymer-wrapped concrete structures Torsional surface waves in an initially stressed anisotropic porous medium Polynomial chaos decomposition for the simulation of non-gaussian nonstationary stochastic processes Eective hybrid/mixed nite elements for folded-plate structures Analytic solution for nite transversely isotropic circular cylinders under the axial point load test Formulation of cracked beam element for structural analysis Element-free method based on lagrange polynomial A boundary element analysis of quasi-brittle solids containing cracks Similarity shapes of an inclined, partially lled membrane container 128(2) 2002 Dennis ST. Baylot JT. Woodson SC. Ead SA. Rajaratnam N. Sfer D. Carol I. Gettu R. Etse G. Wu JH. Chwang AT. Feng MQ. De Flaviis F. Kim YJ. Dey S. Sarkar MG. Sakamoto S. Ghanem R. Duan M. Miyamoto Y. Wei XX. Chau KT. Viola E. Nobile L. Federici L. Suetake Y. Qin F. Cen ZZ. Fung TC. Wang CY. Journal of Engineering Mechanics-ASCE 254 264 280 287 296 308 318 328 340 351 359 369 371 376 377 Size eect on strength of oating sea ice under vertical line load Study of passive deck-aps utter control system on full bridge model. i: theory Study of passive deck-aps utter control system on full bridge model. ii: results Protecting base-isolated structures from near-eld ground motion by tuned interaction damper Postbuckling of shear deformable laminated cylindrical shells Earthquake response and energy evaluation of inelastic structures Spectral analysis and parametric study of stochastic pavement loads Dynamics of nonviscously damped linear systems Bayesian modal updating using complete input and incomplete response noisy measurements Reducing dispersion of linear triangular elements for the helmholtz equation Time-harmonic analysis of wave propagation in unbounded layered strata with zigzag boundaries Addendum to "why did the world trade center collapse? - simple analysis" Graphical relationship among lame ellipsoid and mohr's circles. a graphical view of mohr's circles Discussion of "structural damage detection from modal strain energy change" by z. y. shi, s. s. law, and l. m. zhang Closure to "structural damage detection from modal strain energy change" by z. y. shi, s. s. law, and l. m. zhang 128(3) 2002 Bazant ZP. Guo ZY. Omenzetter P. Wilde K. Fujino Y. Omenzetter P. Wilde K. Fujino Y. Zhang YF. Iwan WD. Shen HS. Wong KKF. Yang R. Sun L. Kennedy TW. Adhikari S. Yuen KV. Katafygiotis LS. Harari I. Nogueira CL. Park SH. Tassoulas JL. Bazant ZP. Zhou Y. Montans FJ. Ren WX. De Roeck G. Shi ZY. Law SS. Zhang LM. Journal of Fluid Mechanics 1 35 67 97 131 Numerical investigation of the interaction of the klebano-mode with a tollmienschlichting wave The eects of heat release on the energy exchange in reacting turbulent shear ow The two-sided lid-driven cavity: experiments on stationary and time-dependent ows Experimental investigation of density uctuations in high-speed jets and correlation with generated noise Stratied kolmogorov ow 450 2002 Fasel HF. Livescu D. Jaberi FA. Madnia CK. Blohm CH. Kuhlmann HC. Panda J. Seasholtz RG. Balmforth NJ. Young YN. 169 201 207 235 259 287 297 317 343 377 Start-up ows in a three-dimensional rectangular driven cavity of aspect ratio 1 : 1 : 2 at re=1000 Spatial versions of the zakharov and dysthe evolution equations for deep-water gravity waves Oscillating structures in a stretched-compressed vortex Instability of an annular jet surrounded by a viscous gas in a pipe Direct numerical simulation of turbulent channel ow with permeable walls A new model for shallow water in the low-rossby-number limit Convection in a spherical capacitor Some observations of the eects of micro-organisms growing on the bed of an open channel on the turbulence properties Aerodynamic ow-vectoring of a planar jet in a co-owing stream A study of the ow-eld evolution and mixing in a planar turbulent jet using direct numerical simulation 21 Guermond JL. Migeon C. Pineau G. Quartapelle L. Kit E. Shemer L. Abid M. Andreotti B. Douad S. Nore C. Chen JN. Lin SP. Hahn S. Je J. Choi H. Ford R. Malham SJA. Oliver M. Amara K. Hegseth J. Nikora VI. Goring DG. Biggs BJF. Lim DW. Redekopp LG. Stanley SA. Sarkar S. Mellado JP. Journal of Fluid Mechanics 1 35 99 145 169 Bragg scattering of random surface gravity waves by irregular seabed topography Subcritical transition in channel ows Dependence of the non-stationary form of yaglom's equation on the schmidt number A numerical investigation of solitary internal waves with trapped cores formed via shoaling Generation of slow large scales in forced rotating stratied turbulence Fluidization of 1204 spheres: simulation and experiment 193 203 Wilton ripples generated by a moving pressure distribution Sand bars in tidal channels part 2. tidal meanders 239 Density-driven unstable ows of miscible uids in a hele-shaw cell 261 Density-driven instabilities of miscible uids in a hele-shaw cell: linear stability analysis of the three-dimensional stokes equations Inclined turbulent fountains Transient motion of a conned stratied uid induced simultaneously by sidewall thermal loading and vertical throughow Optimal perturbations in a four-vortex aircraft wake in counter-rotating conguration A study of compressibility eects in the high-speed turbulent shear layer using direct simulation The ejecta sheet generated by the impact of a drop The turbulent/non-turbulent interface bounding a far wake Four-phase merging in sessile compound drops Force on a body in a continuously stratied uid. part 1. circular cylinder 109 283 295 319 329 373 383 411 421 451 2002 Fabrice A. Herbers THC. Chapman SJ. Orlandi P. Antonia RA. Lamb KG. Smith LM. Walee F. Pan TW. Joseph DD. Bai R. Glowinski R. Sarin V. Vanden-Broeck JM. Solari L. Seminara G. Lanzoni S. Marani M. Rinaldo A. Fernandez J. Kurowski P. Petitjeans P. Meiburg E. Graf F. Meiburg E. Hartel C. Bloomeld LJ. Kerr RC. Park JS. Hyun JM. Fabre D. Jacquin L. Loof A. Pantano C. Sarkar S. Thoroddsen ST. Bisset DK. Hunt JCR. Rogers MM. Mahadevan L. Adda-Bedia M. Pomeau Y. Ermanyuk EV. Gavrilov NV. Journal of Fluid Mechanics 1 25 39 61 97 123 145 163 189 199 231 263 293 303 325 Revisiting the 1954 suspension experiments of r. a. bagnold Salt ngers at low rayleigh numbers Probing structures in channel ow through so(3) and so(2) decomposition Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice boltzmann method Stability of a buoyancy-driven coastal current at the shelf break Stability of steep gravity-capillary solitary waves in deep water Inertially driven inhomogeneities in violently collapsing bubbles: the validity of the rayleigh-plesset equation Electrohydrodynamic stability: taylor-melcher theory for a liquid bridge suspended in a dielectric gas High-reynolds-number turbulence in small apparatus: grid turbulence in cryogenic liquids Transport enhancement mechanisms in open cavities Improvement of the stokesian dynamics method for systems with a nite number of particles A super-rotating shear layer in magnetohydrodynamic spherical couette ow Shocks in sand owing in a silo Instability of a bed of particles sheared by a viscous ow The actively controlled jet in crossow 452 2002 Hunt ML. Zenit R. Campbell CS. Brennen CE. Krishnamurti R. Jo YH. Stocchino A. Biferale L. Lohse D. Mazzitelli IM. Toschi F. Sankaranarayanan K. Shan X. Kevrekidis IG. Sundaresan S. Cenedese C. Linden PF. Calvo DC. Akylas TR. Lin H. Storey BD. Szeri AJ. Burcham CL. Saville DA. White CM. Karpetis AN. Sreenivasan KR. Horner M. Metcalfe G. Wiggins S. Ottino JM. Ichiki K. Dormy E. Jault D. Soward AM. Samadani A. Mahadevan L. Kudrolli A. Charru F. Mouilleron-Arnould H. M'Closkey RT. King JM. Cortelezzi L. Karagozian AR. 22 337 361 371 405 425 On stationary solutions for free quasi-parallel mixing layers with a longitudinal magnetic eld Scaling of acceleration in locally isotropic turbulence Constitutive laws in liquid-uidized beds Gravitaxis in motile micro-organisms: the role of fore-aft body asymmetry Shear stress of a monolayer of rough spheres Journal of Fluid Mechanics 1 21 39 57 109 133 153 177 201 239 263 289 315 345 371 395 411 427 Using surfactants to control the formation and size of wakes behind moving bubbles at order-one reynolds numbers Ferromagnetic rotating couette ow: the role of magnetic viscosity Boundary layer development on a semi-innite suddenly heated vertical plate Coherent structure generation in near-wall turbulence Rayleigh-taylor instability of viscoelastic drops at high weber numbers Friction law for dense granular ows: application to the motion of a mass down a rough inclined plane Long-wave instabilities of non-uniformly heated falling lms Oblique transition in a laminar blasius boundary layer Large-eddy simulation of the turbulent ow through a heated square duct A study of three-dimensional gravity currents on a uniform slope Spatial variations of a passive tracer in a random wave eld Generation of sound and instability waves due to unsteady suction and injection Moderate-reynolds-number ow in a wall-bounded porous medium Rayleigh-benard convection in liquid metal layers under the inuence of a horizontal magnetic eld The propagation of a gravity current into a linearly stratied uid Velocity uctuations in a homogeneous dilute dispersion of high-reynolds-number rising bubbles Analytic solutions of the temperature distribution in blasius viscous ow problems Coalescence of sessile drops Journal of Fluid Mechanics 1 21 47 71 113 145 203 235 263 287 327 345 365 387 403 419 Modelling the morning glory of the gulf of carpentaria Weakly stratied laminar ow past normal at plates The onset of chaos in vortex sheet ow Vertical structure in stratied wakes with high initial froude number Experimental study of a jet in a crossow at very low reynolds number Collision and rebound of small droplets in an incompressible continuum gas The velocity eld under breaking waves: coherent structures and turbulence A lubrication model of coating ows over a curved substrate in space Slip velocity and lift A vlasov equation for pressure wave propagation in bubbly uids Uniform steady free-surface ow in heterogeneous porous formations The motion generated by a rising particle in a rotating uid - numerical solutions. part 2. the long container case On converging shock waves of spherical and polyhedral form Spectral solution of time-dependent shallow water hydroelasticity Do true elevation gravity-capillary solitary waves exist? a numerical investigation Stretching eects on the three-dimensional stability of vortices with axial ow Journal of Fluids & Structures 123 137 153 175 Dynamics of an in-line tube array subjected to steam-water cross-ow. part i: two-phase damping and added mass Dynamics of an in-line tube array subjected to steam-water cross-ow. part i: unsteady uid forces Dynamics of an in-line tube array subjected to steam-water cross-ow. part iii: uidelastic instability tests and comparison with theory Flow visualization around a circular cylinder near to a plane wall Shukhman IG. Hill RJ. Duru P. Nicolas M. Hinch J. Guazzelli E. Roberts AM. Deacon FM. Wilson HJ. Davis RH. 453 2002 Wang YP. Papageorgiou DT. Maldarelli C. Hart JE. Patterson JC. Graham T. Schopf W. Armeld SW. Schoppa W. Hussain F. Joseph DD. Beavers GS. Funada T. Pouliquen O. Forterre Y. Miladinova S. Slavtchev S. Lebon G. Legros JC. King RA. Breuer KS. Vazquez MS. Metais O. Ross AN. Linden PF. Dalziel SB. Weichman PB. Glazman RE. Wu XS. Hill RJ. Koch DL. Burr U. Moller U. Maxworthy T. Leilich J. Simpson JE. Meiburg EH. Risso F. Ellingsen K. Liao SJ. Campo A. Andrieu C. Beysens DA. Nikolayev VS. Pomeau Y. 454 2002 Porter A. Smyth NF. Castro IP. Krasny R. Nitsche M. Spedding GR. Camussi R. Guj G. Stella A. Gopinath A. Koch DL. Melville WK. Veron F. White CJ. Roy RV. Roberts AJ. Simpson ME. Joseph DD. Ocando D. Smereka P. Amir O. Dagan G. Minkov E. Ungarish M. Israeli M. Schwendeman DW. Meylan MH. Champneys AR. Vanden-Broeck JM. Lord GJ. Delbende I. Rossi M. Le Dizes S. 16(2) 2002 Nakamura T. Hirota K. Watanabe Y. Mureithi NW. Kusakabe T. Takamatsu H. Mureithi NW. Nakamura T. Hirota K. Murata M. Utsumi S. Kusakabe T. Takamatsu H. Hirota K. Nakamura T. Kasahara J. Mureithi NW. Kusakabe T. Takamatsu H. Price SJ. Sumner D. Smith JG. Leong K. Paidoussis MP. 193 213 229 247 263 Dynamics of mooring cables in random seas Experimental study on large-amplitude vibrations of water-lled circular cylindrical shells Two-dimensional vortex-induced vibration of cable suspensions Mechanism of mode selection for taylor vortex ow between coaxial conical rotating cylinders Near-wake ow structure of a cylinder with a helical surface perturbation Sarkar A. Taylor RE. Amabili M. Garziera R. Negri A. Kim WJ. Perkins NC. Noui-Mehidi MN. Ohmura N. Kataoka K. Chyu CK. Rockwell D. Journal of Intelligent Material Systems & Structures 923 930 High bandwidth tunability in a smart vibration absorber Rechargeable lithium batteries for powering piezoelectric devices 936 945 Vibration control of a mr seat damper for commercial vehicles Smart uid damping: shaping the force/velocity response through feedback control Characterization of piezoelectric wafer active sensors Shape memory elements in bending: inuence of the shape of their cross-section 959 977 11(12) 2000 Flatau AB. Dapino MJ. Calkins FT. Salloux K. Lim J. Dunn B. Chaplya PM. Carman GP. Choi SB. Nam MH. Lee BK. Sims ND. Stanway R. Johnson AR. Peel DJ. Bullough WA. Giurgiutiu V. Zagrai AN. Kafka V. Vokoun D. Journal of Intelligent Material Systems & Structures 3 11 41 Robust pole assignment for vibration control of exible structures Limitations of using membrane theory for modeling pvdf patches on inatable structures Mechanism-based phenomenological models for the pseudoelastic hysteresis behavior of shape memory alloys Eigenstrain techniques for modeling adaptive structures. i: active stiness tailoring A continuous sensor to measure acoustic waves in plates 57 Electrorheological eects of er gels containing iron particles 21 31 12(1) 2001 Okubo H. Ichikawa H. Williams RB. Austin EM. Inman DJ. Malovrh B. Gandhi F. Alghamdi AAA. Dasgupta A. Sundaresan MJ. Ghoshal A. Martin WN. Schulz MJ. Liu B. Shaw MT. Journal of Intelligent Material Systems & Structures 67 69 79 93 105 117 127 133 Special issue: third international conference on mechanics and materials in design symposium on smart materials and adaptive structures - preface A nite element analysis of second order eects on the frequency response of a saw device A micromechanics-based hysteresis model for ferroelectric ceramics Control of transient thermoelastic displacement in a piezoelectric based intelligent plate Wave propagation in electromechanical structures: induced by surface-bonded piezoelectric actuators Wave propagation in electromechanical structures: induced by embedded piezoelectric actuators Energy conversion in shape memory alloy heat engine - part i: theory Energy conversion in shape memory alloy heat engine - part ii: simulation 12(2) 2001 Wang X. Xu GS. Jiang Q. Li J. Weng GJ. Ashida F. Noda N. Wang XD. Huang GL. Wang XD. Huang GL. Zhu JJ. Liang NG. Liew KM. Huang WM. Zhu JJ. Liang NG. Huang WM. Liew KM. Journal of Intelligent Material Systems & Structures 143 157 161 165 183 191 Feedback control of the bending response of ionic polymer actuators Single axis piezoceramic gimbal Flow of magnetorheological uids Micromechanical modeling of a composite containing piezoelectric and shape memory alloy inclusions Adaptive imperfect column with piezoelectric actuators Vibration suppression via smart structures across a temperature range 23 12(3) 2001 Mallavarapu K. Leo DJ. Horner G. Taleghani B. Lange U. Richter L. Zipser L. Jiang B. Batra RC. Alghamdi AAA. Hegewald T. Inman DJ. 24 Journal of Intelligent Material Systems & Structures 207 209 215 223 229 235 247 259 265 271 277 283 289 295 The eleventh international conference on adaptive structures and technologies preface Decentralized vibration control and coupled aeroservoelastic simulation of helicopter rotor blades with adaptive airfoils Performance comparison between piezoelectric and elastomeric lag dampers on ground resonance stability of helicopter Miniature free-fall sensors Material structure design of stress-dependent adaptive stiness Use of piezoelectric shear response in adaptive sandwich shells of revolution - part 1: theoretical formulation Use of piezoelectric shear response in adaptive sandwich shells of revolution - part 2: nite element implementation Specic damping capacity of multiphase unidirectional hybrid ber composites Improved surface treatment of sma foils and damage suppression of sma-foil embedded cfrp laminates Mechanical property of metallic closed cellular materials containing organic material for passive damping and energy-absorbing systems Simultaneous measurement of strain and temperature of structures using ber optic sensor Thermomechanical properties of polyurethane-shape memory polymer foam Two-way shape memory behavior obtained by combined loading training Analytical study on training eect of pseudoelastic transformation of shape memory alloys in cyclic loading 12(4) 2001 Matsuzaki Y. Konstanzer P. Grohmann B. Kroplin B. Kim SJ. Yun CY. Hsu YH. Lee CK. Tanaka M. Todoh M. Oki K. Naomi A. Benjeddou A. Gorge V. Ohayon R. Benjeddou A. Gorge V. Ohayon R. Baburaj V. Matsuzaki Y. Nae FA. Ikeda T. Ogisu T. Ando N. Takaki J. Okabe T. Takeda N. Kishimoto S. Shinya N. Kang HK. Ryu CY. Hong CS. Kim CG. Tobushi H. Okumura K. Endo M. Hayashi S. Tokuda M. Sugino S. Inaba T. Naito H. Sato J. Funami K. Matsuzaki Y. Ikeda T. Journal of Microelectromechanical Systems 2 12 20 27 36 45 54 61 68 78 85 91 An extraction-based verication methodology for mems Measurements and modeling of two-phase ow in microchannels with nearly constant heat ux boundary conditions Design considerations of rectangular electrostatic torsion actuators based on new analytical pull-in expressions The strain gradient eect in microelectromechanical systems (mems) Electroosmotic ow control in complex microgeometries Fabrication and characterization of hydrogel-based microvalves Ink-jet printed nanoparticle microelectromechanical systems A passive humidity monitoring system for in situ remote wireless testing of micropackages Three-dimensional thin-lm shape memory alloy microactuator with two-way effect A bidirectional magnetic microactuator using electroplated permanent magnet arrays Micromachining of glass inertial sensors High-cycle fatigue of single-crystal silicon thin lms (vol 10, pg 593, 2001) 11(1) 2002 Baidya B. Gupta SK. Mukherjee T. Zhang L. Koo JM. Jiang L. Asheghi M. Goodson KE. Santiago JG. Kenny TW. Degani O. Nemirovsky Y. Xue ZY. Saif MTA. Huang YG. Dutta P. Beskok A. Warburton TC. Liu RH. Yu Q. Beebe DJ. Fuller SB. Wilhelm EJ. Jacobson JA. Harpster TJ. Hauvespre S. Dokmeci MR. Naja K. Gill JJ. Ho K. Carman GP. Cho HJ. Ahn CH. Belloy E. Sayah A. Gijs MAM. Muhlstein CL. Brown SB. Ritchie RO. Journal of Non-Newtonian Fluid Mechanics 1 45 65 A new nite element scheme using the lagrangian framework for simulation of viscoelastic uid ows A nite deformation formulation of the 3-parameter viscoelastic uid Highly elastic solutions for oldroyd-b and phan-thien/tanner uids with a nite volume/element method: planar contraction ows 103(1) 2002 Petera J. Balan C. Tsakmakis C. Aboubacar M. Matallah H. Webster MF. Journal of Sound & Vibration 417 429 447 465 483 499 A method to predict acoustic radiation from an enclosed multicavity structure Analysis of the response of a cracked jecott rotor to axial excitation Vibration and stability of annular plates in non-linear creep conditions Asymptotic approach for non-linear periodical vibrations of continuous structures Dynamic response of two rotors connected by rigid mechanical coupling with parallel misalignment Analysis of the exural vibration of a thin-plate box using a combination of nite element analysis and analytical impedances 249(3) 2002 Wu JH. Chen HL. Darpe AK. Chawla A. Gupta K. Gajewski A. Andrianov IV. Danishevskyy VV. Al-Hussain KM. Redmond I. Grice RM. Pinnington RJ. 529 543 557 575 599 606 611 622 Chaotic dynamics of repeated impacts in vibratory bowl feeders Stochastic dynamic sensitivity of uncertain structures subjected to random earthquake loading On the origins and development of mobility and impedance methods in structural dynamics [review] Development and validation of reaction wheel disturbance models: empirical model On the behavior of dissipative time integration methods near the resonance condition Dynamic analysis of an active exible suspension system Robustness analysis of an environmental active noise control system Preliminary computations for chatter control in end milling Han I. Lee Y. Bhattacharyya B. Chakraborty S. Gardonio P. Brennan MJ. Masterson RA. Miller DW. Grogan RL. Cannillo V. Mancuso M. Sun YG. Song KJ. Mao YH. Yang J. Tan SE. Gan WS. Semercigil SE. Chen LA. Journal of Sound & Vibration 635 649 663 679 701 719 743 775 785 815 824 828 832 Alternative vibration protecting systems for men-operators of transport machines: modern level and prospects Experimental study on the vortex-induced vibration of towed pipes Structural response of laminated composite shells subjected to blast loading: comparison of experimental and theoretical methods Noise generated by a coanda wall jet circulation control device Non-linear vibration absorber for a system under sinusoidal and random excitation: experiments Merging sensor data from multiple measurement set-ups for non-stationary subspace-based modal analysis Non-linear modelling of rotor dynamic systems with squeeze lm dampers - an eÆcient integrated approach A synthetic analysis on design of optimum control for an optimized intelligent structure A comparison of three techniques using steady state data to identify non-linear modal behavior of an externally excited cantilever beam Eect of non-ideal boundary conditions on the vibrations of continuous systems On the propagation of plane sound waves in ducts carrying an incompressible axial mean ow having an arbitrary velocity prole Road traÆc noise annoyance and window orientation in dwellings Comments on "stochastic model on a rattling system" 249(4) 2002 Lee CM. Goverdovskiy VN. Hong S. Choi YR. Park JB. Park YK. Kim YH. Turkmen HS. Howe MS. Cuvalci O. Ertas A. Ekwaro-Osire S. Cicek I. Mevel L. Basseville M. Benveniste A. Goursat M. Bonello P. Brennan MJ. Holmes R. Yan YJ. Yam LH. Doughty TA. Davies P. Bajaj AK. Pakdemirli M. Boyaci H. Dokumaci E. Rylander R. Bjorkman M. Dai DC. Journal of Sound & Vibration 835 849 867 885 899 909 921 939 955 971 995 999 1011 Adaptive-passive absorbers using shape-memory alloys Physical interpretation of the proper orthogonal modes using the singular value decomposition Selection of training samples for model updating using neural networks Acoustic power suppression of a panel structure using h-innity output feedback control Oscillation-sliding in a modied van der pol-duÆng electronic oscillator Normal mode localization for a two degrees-of-freedom system with quadratic and cubic non-linearities Dynamic traction vector eld estimation in a structure using hybrid strain analysis Wavenumber prediction of waves in buried pipes for water leak detection Extraction of structural system matrices from an identied state-space system using the combined measurements of dva A new galerkin-based approach for accurate non-linear normal modes through invariant manifolds Period preservation and period adjustment in the numerical integration of the linear and non-linear equations of motion Vibration parameters for damage detection in structures Comments on "vibration analysis of thin cylindrical shells using the wave propagation approach" 25 249(5) 2002 Williams K. Chiu G. Bernhard R. Kerschen G. Golinval JC. Chang CC. Chang TYP. Xu YG. To WM. Sivrioglu S. Tanaka N. Yuksek I. Algaba A. Fernandez-Sanchez F. Freire E. Gamero E. Rodriguez-Luis AJ. Bhattacharyya R. Jain P. Nair A. Sehlstedt N. Muggleton JM. Brennan MJ. Pinnington RJ. Ko WJ. Hung CF. Pesheck E. Pierre C. Shaw SW. Fried I. Palacz M. Krawczuk M. Wang C. Lai JCS. 26 Journal of Sound & Vibration 1 5 9 23 31 41 47 53 65 75 83 91 101 107 115 119 129 139 145 151 157 161 169 175 Fourth japanese-swedish noise symposium on medical eects, rosenon, stockholm, sweden, 16-19 august 2000 Current research topics and problems: the role of icben Diagnostic system based on the human auditory-brain model for measuring environmental noise - an application to railway noise Psycho-circulatory responses caused by listening to music, and exposure to uctuating noise or steady noise Duration sensation when listening to bandpass noises Relation between the overall impression of the sound environment and types and loudness of environmental sounds Loudness of sharply (2068 db/octave) ltered noises in relation to the factors extracted from the autocorrelation function Annoyance and spectral contrast are cues for similarity and preference of sounds Psycho-acoustic characters of relevance for annoyance of wind turbine noise Sleep time monitoring by accelerometer in two subjects for 1 year The eect of dierent kinds of noise on the quality of sleep under the controlled conditions Dierent eects of road traÆc noise and frogs' croaking on night sleep Habituation of sleep to road traÆc noise observed not by polygraphy but by perception Habituation of sleep to a ship's noise as determined by actigraphy and a sleep questionnaire Protecting against noise trauma by sound conditioning Self-evaluation scores of hearing diÆculties and quality of life components among retired workers with noise-related hearing loss Population-based questionnaire survey on health eects of aircraft noise on residents living around us airelds in the ryukyus - part 1: an analysis of 12 scale scores Population-based questionnaire survey on health eects of aircraft noise on residents living around us airelds in the ryukyus - part ii: an analysis of the discriminant score and the factor score Distribution of blood pressure data from people living near an airport Adverse health eects in relation to urban residential soundscapes Road traÆc noise inuenced by road bumps Comparison of community response to road traÆc noise in japan and sweden part i: outline of surveys and dose-response relationships Comparison of community response to road traÆc noise in japan and sweden part ii: path analysis Planning consequences of the maximum db(a) concept - a perspective 250(1) 2002 Rylander R. Ando Y. Gjestland T. Sakai H. Hotehama T. Ando Y. Prodi N. Pompoli R. Sakamoto H. Hayashi F. Sugiura S. Tsujikawa M. Ando Y. Saifuddin K. Sato S. Kawai K. Yano T. Sato S. Kitamura T. Ando Y. Berglund B. Hassmen P. Preis A. Waye KP. Ohrstrom E. Kawada T. Kuroiwa M. Sasazawa Y. Suzuki S. Tamura Y. Kuwano S. Mizunami T. Namba S. Morinaga M. Sasazawa Y. Xin P. Suzuki S. Kawada T. Kuroiwa M. Tamura Y. Kuroiwa M. Xin P. Suzuki S. Sasazawa Y. Kawada T. Tamura Y. Tamura Y. Horiyasu T. Sano Y. Chonan K. Kawada T. Sasazawa Y. Kuroiwa M. Suzuki S. Niu X. Canlon B. Miyakita T. Ueda A. Zusho H. Kudoh Y. Miyakita T. Matsui T. Ito A. Tokuyama T. Hiramatsu K. Osada Y. Yamamoto T. Hiramatsu K. Matsui T. Miyakita T. Ito A. Tokuyama T. Osada Y. Yamamoto T. Goto K. Kaneko T. Skanberg A. Ohrstrom E. Rylander R. Bjorkman M. Sato T. Yano T. Bjorkman M. Rylander R. Yano T. Sato T. Bjorkman M. Rylander R. Rylander R. Bjorkman M. Journal of Sound & Vibration 181 197 215 229 247 277 299 323 339 351 356 368 Measurement of the viscoelastic properties of damping materials: adaptation of the wave propagation method to test samples of short length Reducing operator-induced machine vibration using a complex pole/zero prelter Dispersion of waves in immersed laminated composite hollow cylinders Chaos and multiple periods in an unsymmetrical spring and damping system with clearance Energy transfer for high frequencies in built-up structures Whistles with a generic sidebranch: production and suppression Eects of end cap and aspect ratio on transmission of sound across a truss-like periodic double panel Combination of nite and boundary element methods in investigation and prediction of load-controlled noise of power transformers Normal modes of a non-linear clamped-clamped beam Coupling loss factors for coupled anisotropic plates Stability analysis of spinning stepped-shaft workpieces in a turning process Natural frequencies of tensioned pipes conveying uid and carrying a concentrated mass 250(2) 2002 Lemerle P. Ingram GA. Franchek MA. Chiu GTC. Xi ZC. Liu GR. Lam KY. Shang HM. Hossain MZ. Mizutani K. Sawai H. Le Bot A. Selamet A. Kurniawan D. Knotts BD. Novak JM. El-Raheb M. Wagner P. Rausch M. Kaltenbacher M. Landes H. Lerch R. Anger J. Gerth J. Boss P. Xie WC. Lee HP. Lim SP. Bosmans I. Vermeir G. Mees P. Wang ZC. Cleghorn WL. Oz HR. Evrensel CA. 27 Journal of Sound & Vibration 379 401 415 431 445 465 485 503 519 541 567 569 575 Measurement and analysis of modulated doublet mode response in mock bladed disks Dynamic stability of skew plates subjected to aerodynamic and random in-plane forces The application of ball-type balancers for radial vibration reduction of high-speed optic disk drives High-frequency radiation of l-shaped plates by a local energy ow approach Dynamic stability problem of a non-prismatic rod An approach to parameter identication for a single-degree-of-freedom dynamical system based on short free acceleration response Active impact control system design with a hydraulic damper Exact buckling and vibration solutions for stepped rectangular plates Passive damping augmentation of a vibrating beam using pseudoelastic shape memory alloy wires Coincidence of thermoelastic and thermoviscous acoustic waves in uid-lled elastic tubes More on generalized harmonic oscillators Transverse vibrations of rectangular plates of generalized anisotropy and discontinuously varying thickness Transverse vibrations of clamped and simply supported circular plates of deformed boundaries 250(3) 2002 Chang JY. Wickert JA. Young TH. Lee CW. Chen FY. Huang WY. Chao CP. Kang JR. Sung CK. Cotoni V. Le Bot A. Jezequel L. Ruta P. Jaksic N. Boltezar M. Kim DH. Park JW. Lee GS. Lee KI. Xiang Y. Wang CM. Gandhi F. Chapuis G. Liang PN. Scarton HA. Hu H. Laura PAA. Gutierrez RH. Gutierrez RH. Laura PAA. Rossi RE. Journal of Sound & Vibration 579 591 609 617 627 649 675 711 723 745 762 Experimental active control of automotive disc brake rotor squeal using dither Control of multi-span beam vibration by a random wave reector Dynamic analysis of delayed damper system in engineering structures Modelling and control with piezoactuators for a simply supported beam under a moving mass An investigation of power ow characteristics of l-shaped plates adopting a substructure approach Forced vibrations of triply coupled, periodically and elastically supported, nite, open-section channels Vibration of a compliant tower in three-dimensions Wave propagation through a cylindrical bore contained in a microstretch elastic medium Model comparison for acoustic scattering by a spherical air bubble in water Loss factors of composite honeycomb sandwich panels Design of a novel cryptosystem based on chaotic oscillators and feedback inversion 250(4) 2002 Cunefare KA. Graf AJ. Xu MB. Huang L. Chen D. Xu H. Sung YG. Wang ZH. Xing JT. Price WG. Yaman Y. Ozdemir O. Han SM. Benaroya H. Kumar R. Deswal S. Wang CC. Ye Z. Renji K. Narayan SS. Shahruz SM. Pradeep AK. Gurumoorthy R. Journal of Strain Analysis for Engineering Design 1 13 21 33 47 59 73 87 Prediction of fold eccentricity in the axial axisymmetric plastic progressive collapse of circular tubes Determination of residual stress using critically refracted longitudinal waves and immersion mode Development of the alternating current stress measurement model for magnetostriction behaviour of mild steel under orthogonal magnetic elds for stress measurement Elastic-plastic analyses for surface cracked plates under combined bending and tension A parametric study of inclusion interaction in particulate- and bre-reinforced materials using the boundary element technique Identication of the sources of non-adiabatic behaviour for practical thermoelastic stress analysis Analysis of neutron diraction strain measurement data from a round robin sample Small sample theory for reliability design 37(1) 2002 Avalle M. Belingardi G. Belahcene F. Lu J. Han S. Brennan FP. Dover WD. Kim YJ. Shim DJ. Choi JB. Knight MG. de Lacerda LA. Henshall JL. Wrobel LC. Quinn S. Dulieu-Barton JM. Daymond MR. Johnson MW. Sivia DS. Xiong J. Shenoi RA. Gao Z. 28 Journal of Thermal Stresses 215 245 265 283 295 Transient thermoelastic analysis of disk brake using the fast fourier transform and nite element method Stabilized ux-based ow/thermal nite element representations with applications to convectively cooled structures An inverse problem of coupled thermoelasticity in predicting heat ux and thermal stresses by strain measurement A macroscopic model for the heat propagation in the microperiodic composite solids State space approach to two-dimensional generalized thermoviscoelasticity with one relaxation time 25(3) 2002 Cho CD. Ahn S. Poon WS. Tamma KK. Yang YC. Chen UC. Chang WJ. Wozniak C. Wierzbicki E. Wozniak M. Ezzat MA. Othman MI. El-Karamany AS. Journal of Thermal Stresses 319 341 363 373 389 Multidisciplinary ow/thermal and induced stresses in convectively cooled structures Thermoelastic interactions in a transversely isotropic elastic medium with a cylindrical hole subjected to ramp-type increase in boundary temperature or load Thermal elastic-plastic stress analysis of symmetric aluminum metal-matrix composite laminated plates under uniformly distributed temperature The inuence of crack-face uid pressure on the fatigue crack propagation due to rolling contact with frictional heat Thermal stress analysis in thermopiezoelastic strip with an edge crack 25(4) 2002 Poon WS. Kanapady R. Mohan RV. Tamma KK. Mukhopadhyay S. Sayman O. Sayman S. Goshima T. Ishihara S. Shimizu M. Niraula OP. Noda N. Journal of Vibration & Control 3 13 19 41 51 69 87 Prediction of structure-borne sound in orthotropic plates for far-eld conditions Stability for hopeld neural networks with time delay Enhanced proper orthogonal decomposition for the modal analysis of homogeneous structures A mathematical model for pseudoelasticity of shape memory alloy and its application in passive control Vibration analysis of rotor for crack identication Vibration control of unknown exible beam structures Nonlinear modeling, experimental verication, and theoretical analysis of a hydraulic engine mount 8(1) 2002 Mandal NK. Leong MS. Abd Rahman R. Wang LS. Xu DY. Han S. Feeny BF. Wei Z. Ma HY. Sun DC. Saavedra PN. Cuitino LA. Mohammad KS. Al-Dmour AS. Jazar GN. Golnaraghi MF. JSME International Journal Series A -Solid Mechanics & Material Engineering 1 2 8 Special issue on creep and fatigue at elevated temperatures Creep behavior of ir-nb and ir-zr refractory superalloys Creep behavior of ir-nb-ni two-phase refractory superalloy 14 Creep behavior of 8cr2wvta martensitic steel designed for fusion demo reactor* (an assessment on helium embrittlement resistance) Creep behavior of orthorhombic ti(2)ainb based intermetallic alloys Eects of w and co on the microstructure and creep strength of the precipitation strengthened 15cr ferritic steels Inuence of pre-aging on creep rupture strength of tungsten alloyed 9cr ferritic steel and creep damage evaluation by electrochemical method Nondestructive evaluation of creep damage using leaky surface acoustic wave technique High temperature low cycle fatigue of 2 1/4 cr1mo steels: role of microstructure and eect of environment Study on creep-fatigue life of irradiated austenitic stainless steel 20 25 30 39 46 51 57 65 72 77 Thermal fatigue in thermal barrier coating On time-dependent crack growth parameters in plasticity and creep elds Evaluation of creep damage due to void growth under triaxial stress states in the design of steam turbine components Shear correction factors in creep-damage analysis of beams, plates and shells 45(1) 2002 Nitta A. Yamabe-Mitarai Y. Nakazawa S. Harada H. Gu YF. Yamabe-Mitarai Y. Nakazawa S. Harada H. Yamamoto N. Murase Y. Nagakawa J. Shiba K. Tang F. Nakazawa S. Hagiwara M. Toda Y. Seki K. Kimura K. Abe F. Komazaki S. Kishi S. Shoji T. Kumazawa T. Higuchi K. Suzuki K. Yokono Y. Nagano Y. Mukai K. Imanaka T. Vogt JB. Sosa JL. Argillier S. Ioka I. Miwa Y. Tsuji H. Yonekawa M. Takada F. Hoshiya T. Zhou YC. Hashida T. Kim KS. Han C. Wichtmann A. Altenbach H. Naumenko K. 84 90 98 104 110 Finite element creep continuum damage mechanics analysis of pressurised pipe bends with ovality The use of cdm analysis techniques in high temperature creep failure of welded structures Advances in the use of stress relaxation data for design and life assessment in combustion turbines Development of a ller metal for weldments of a ni-cr-w superalloy with high creep strength Development of 18cr-9ni-w-nb-v-n austenitic stainless steel tube for thermal power boilers Hyde TH. Yaghi A. Becker AA. Earl PG. Hayhurst DR. Wong MT. Vakili-Tahami F. Woodford DA. Kurata Y. Saito T. Tsuji H. Takatsu T. Shindo M. Nakajima H. Ishitsuka T. Mimura H. JSME International Journal Series C -Mechanical Systems Machine Elements & Manufacturing 914 920 928 937 946 952 958 964 972 982 990 996 1005 1013 1021 1031 1041 1051 1059 1065 1072 1082 1089 1097 1103 1111 1117 1125 1133 Eect of actin lament on deformation-induced ca2+ response in osteoblast-like cells Dynamic response to mechanical stimulation in myoblasts Large deformation mechanics of plasma membrane chained vesicles in cells Improvement in the viability of cryopreserved cells by microencapsulation Thrust force characteristics of propulsion mechanism modeled on bending mechanism of eukaryotic agella in water Optimum shape of a agellated microorganism Comparison between observation and boundary element analysis of bacterium swimming motion Proposal of a deformable erythrocyte model and numerical analysis of shear ow of blood Measurement of surface topography of endothelial cell and wall shear stress distribution on the cell Numerical simulation system for blood ow in the cerebral artery using ct imaging data Flow around cells adhered to a microvessel wall. iii. eects of neighboring cells in channel ow Changes in water ltration velocity and wall structure of the rabbit common carotid artery after removal of the adventitia Mass transport in pulsatile ow through asymmetric stenosis Relationship between intraventricular ow patterns and the shapes of the aliasing area in color m-mode doppler echocardiograms - a cfd study with an axisymmetric, model of the lv The eect of creating a moderate stenosis on the localization of intimal thickening in the common carotid artery of the rabbit fed on a cholesterol-rich diet Fundamental investigation for developing drug delivery systems and bioprocess with shock waves and bubbles - (numerical analysis of deformation of cell model and observation of bubble behaviour near the cell-membrane model) Secondary, ow augmentation during intermittent oscillatory ow in model human central airways Mechanical evaluation of reconstructed structures after total sacrectomy and their improvement Study on treatment with respect to idiopathic scoliosis - (sensitivity analysis based on buckling theory) Thermoelastic femoral stress imaging for experimental evaluation of hip prosthesis design Development of a nite element model of the human shoulder to investigate the mechanical responses and injuries in side impact Dynamic evaluation of the contact characteristics and three-dimensional motion for the ankle joint with lateral ligament injuries Eects of knee and ankle movements on foot impact forces in human walking Eect of depth of conical-shaped tympanic membrane on middle-ear sound transmission The wing apparatus and apping behavior of hymenoptera Interlaminar reinforcement mechanism in a beetle fore-wing Experimental study on oscillating wing for propulsor with bending mechanism modeled on caudal muscle-skeletal structure of tuna A method for gait analysis in a daily living environment by body-mounted instruments A study of an emg-based exoskeletal robot for human shoulder motion support 29 44(4) 2001 Adachi T. Murai T. Hoshiai S. Tomita Y. Murakami S. Homma K. Atomi Y. Kosawada T. Sanada K. Takano T. Matsumoto Y. Morinaga Y. Ujihira M. Oka K. Tanishita K. Kobayashi S. Nakasone M. Furihata K. Morikawa H. Fujita T. Kawai T. Goto T. Masuda S. Terada K. Takano Y. Ishikawa T. Kawabata N. Tachibana M. Fukushima S. Nagatsu A. Kaibara M. Oka K. Tanishita K. Torii R. Oshima M. Kobayashi T. Takagi K. Sugihara-Seki M. Wada S. Kaichi M. Karino T. Ishikawa T. Oshima S. Yamane R. Nakamura M. Wada S. Mikami T. Kitabatake A. Karino T. Wada S. Koujiya M. Karino AT. Tamagawa M. Yamanoi I. Matsumoto A. Tanaka G. Kotaro OKA. Tanishita K. Sakamoto J. Oda J. Nagashima Y. Yoshida A. Murakami H. Kawahara N. Tomita K. Takeuchi K. Azegami H. Murachi S. Kitoh J. Ishida Y. Kawakami N. Makino M. Hyodo K. Inomoto M. Ma W. Miyakawa S. Tateishi T. Iwamoto M. Miki K. Yang KH. Kawakami K. Omori G. Terashima S. Sakamoto M. Hara T. Tagawa Y. Shiba N. Miyazaki K. Matsuo S. Inoue A. Yamashita T. Koike T. Wada H. Kobayashi T. Sudo S. Tsuyuki K. Ito Y. Tani J. Ni QQ. Chen JX. Iwamoto M. Kurashiki K. Saito K. Morikawa H. Nakao S. Kobayashi SI. Ohtaki Y. Sagawa K. Inooka H. Kiguchi K. Iwami K. Watanabe K. Fukuda T. 30 1142 1152 Identication of control parameters for brass player's embouchure by measuring contact pressure on the teeth buccal surface Investigation on a temperature control system modeled after the function of the skin - (on the temperature control system by the operation of ow rate allotment) Kourakata I. Moriyama K. Hara T. Nakamura M. Shoji S. Suzuki R. Yamada E. Meccanica 243 251 265 273 291 297 Wear of an elastic block Similarity solutions for thawing processes with a heat ux condition at the xed boundary Euler's problem revisited: 222 years later On generalised and implicit normality hypotheses Stochastic sensitivity analysis of structures using rst-order perturbation Nonlinearity in uid resonances [review] 36(3) 2001 Villaggio P. Lombardi AL. Tarzia DA. Elishako I. Bodoville G. Ghosh R. Chakraborty S. Bhattacharyya B. Ockendon H. Ockendon JR. Mechanics of Materials 75 97 117 127 An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identication and numerical verication An eective stress elastic-plastic model for unsaturated porous media Two-dimensional analysis on elastic strain energy due to a uniformly eigenstrained supercircular inclusion in an elastically anisotropic material Eect of plastic prestrain on high cycle fatigue of ti-6al-4v 34(2) 2002 Amin AFMS. Alam MS. Okui Y. Loret B. Khalili N. Onaka S. Kobayashi N. Kato M. Lanning DB. Nicholas T. Haritos GK. Mechanics of Structures & Machines 0 1 31 83 103 123 Special issue on symbolic computing in multibody dynamics - preface Symbolic-numeric analysis of exible multibody systems Fully symbolic generation of complex multibody models On the foreshortening eects of a rotating exible beam using dierent modeling methods Symbolic methods for systems of implicit ordinary dierential equations Symbolic programming of a graph-theoretic approach to exible multibody dynamics 30(1) 2002 McPhee J. Claus H. Schiehlen W. Fisette P. Postiau T. Sass L. Samin JC. Piedboeuf JC. Moore B. Schlacher K. Kugi A. Shi PF. McPhee J. Mechanics Research Communications 601 611 617 623 629 637 653 671 679 685 693 703 Attitude drift toward collinearity of a wayward planet Age eect investigation on postural dynamic responses of human body A general solution procedure for coupled systems with arbitrary internal resonances Investigation of laminar ow through solution of inverse problem for heat conduction equation Finite element formulation of 3-d heat transfer problem for orthotropic materials Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena A new approach for the slope stability analysis The state vector solution of axisymmetric biot's consolidation problems for multilayered poroelastic media Bleustein-gulyaev waves in strained piezoelectric ceramics The electrostrictive eect on wave propagation in isotropic solids subjected to initial elds Finite viscoelasticity, plasticity and damage of a class of lled elastomers: constitutive model Closed-form solution for a mode-iii crack at the mid-plane of a piezoelectric layer 28(6) 2001 Rimrott FPJ. Salustri FA. Hoviattalab M. Pakdemirli M. Cialkowski M. Frackowiak A. Kolodziej JA. Yan XQ. Yu ZX. Melnik RVN. Roberts AJ. Thomas KA. Yang HJ. Wang JH. Liu YQ. Wang JG. Fang SS. Yang JS. Simionescu-Panait O. Bikard J. Desoyer T. Li XF. Duan XY. Nonlinear Dynamics 1 3 Untitled - preface Invariant manifolds, nonclassical normal modes, and proper orthogonal modes in the dynamics of the exible spherical pendulum 25(1-3) 2001 Vakakis AF. Georgiou IT. Schwartz IB. 33 49 65 79 95 111 133 157 183 207 221 237 255 275 Normal vibrations in near-conservative self-excited and viscoelastic nonlinear systems Nonlinear normal modes in a system with nonholonomic constraints Nonlinear normal modes of a parametrically excited cantilever beam Normal modes and boundary layers for a slender tensioned beam on a nonlinear foundation The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables Spatially localized models of extended systems Mode localization in dynamics and buckling of linear imperfect continuous structures Dynamics of relative phases: generalised multibreathers Nonlinear modal analysis of structural systems using multi-mode invariant manifolds Localization in nonlinear mistuned systems with cyclic symmetry Mode localization induced by a nonlinear control loop Transition of energy to a nonlinear localized mode in a highly asymmetric system of two oscillators Application of nonlinear normal mode analysis to the nonlinear and coupled dynamics of a oating oshore platform with damping Performance of nonlinear vibration absorbers for multi-degrees-of-freedom systems using nonlinear normal modes Rand RH. Ramani DV. Yabuno H. Nayfeh AH. Pellicano F. Vakakis AF. Manevitch LI. Wittenberg RW. Holmes P. Luongo A. Ahn T. MacKay RS. Sepulchre JA. Pesheck E. Boivin N. Pierre C. Shaw SW. Sextro W. Popp K. Krzyzynski T. M'Closkey RT. Vakakis A. Gutierrez R. Gendelman OV. Falzarano JM. Clague RE. Kota RS. Agnes GS. Inman DJ. Nonlinear Dynamics 293 317 333 355 369 383 Bifurcation analysis of parametrically excited rayleigh-lienard oscillators Dimensional reduction for nonlinear time-delayed systems composed of sti and soft substructures Passive transient wave connement due to nonlinear joints in coupled exible systems Resonance and stochastic layer in a parametrically excited pendulum Local bifurcation control of a forced single-degree-of-freedom nonlinear system: saddle-node bifurcation Fault identication in rotating machinery using the correlation dimension and bispectra 25(4) 2001 Maccari A. Wang ZH. Hu HY. Nayfeh TA. Vakakis AF. Luo ACJ. Ji JC. Wang WJ. Wu ZT. Chen J. Nonlinear Dynamics 1 3 23 45 67 87 In memory of ross m. evan-iwanowski - october 2, 1914-march 18, 2001 An eigenvalue method for calculation of stability and limit cycles in nonlinear systems Hopf bifurcation and stability of periodic solutions for van der pol equation with distributed delay A second-order approximation of multi-modal interactions in externally excited circular cylindrical shells Practical evaluation of invariant measures for the chaotic response of a twofrequency excited mechanical oscillator Nonlinear vibration of plane structures by nite element and incremental harmonic balance method 26(1) 2001 Sinha SC. Somieski G. Liao XF. Wong KW. Wu ZF. Chin CM. Nayfeh AH. Nichols JM. Virgin LN. Chen SH. Cheung YK. Xing HX. Nonlinear Dynamics 105 121 143 163 179 The response of a parametrically excited van der pol oscillator to a time delay state feedback Subcritical hopf bifurcation in the delay equation model for machine tool vibrations Stabilization of the parametric resonance of a cantilever beam by bifurcation control with a piezoelectric actuator Transverse vibrations of a centrally clamped rotating circular disk A survey of rail vehicle track simulations and exible multibody dynamics [review] 31 Mikhlin YV. Morgunov BI. 26(2) 2001 Maccari A. Kalmar-Nagy T. Stepan G. Moon FC. Yabuno H. Saigusa S. Aoshima N. Nayfeh AH. Jilani A. Manzione P. Shabana AA. Sany JR. 32 Nonlinear Dynamics 211 231 253 273 297 The response of a rayleigh-lienard oscillator to a fundamental resonance Eect of unsteady wind ow on galloping of tall prismatic structures Distinguishing periodic and chaotic time series obtained from an experimental nonlinear pendulum Nonlinear dynamics of two-degrees-of-freedom uid conveying elasto-visco-plastic model system Non-local periodic motions of a thin cantilevered rod 26(3) 2001 Maccari A. Abdel-Rohman M. Franca LFP. Savi MA. Terentiev AV. MacEwen KW. Nonlinear Dynamics 309 331 351 371 393 Approximate rst integrals of weakly nonlinear, damped-driven oscillators with one degree of freedom Uniform convergence series to solve nonlinear partial dierential equations: application to beam dynamics Nonlinear frequency response of nonisothermal adsorption systems 3d dynamic modelling of spatial geared systems Thermally induced, nonlinear vibrations of rotating disks 26(4) 2001 Unal G. Filipich CP. Rosales MB. Petkovska M. Wang Y. Cheung HME. Zhang WJ. Saniei N. Luo ACJ. Nonlinear Dynamics 1 19 55 69 87 Eect of nonlinear stiness on the motion of a exible pendulum Analysis on double hopf bifurcation using computer algebra with the aid of multiple scales Multiple equilibria and their eects on impact damage in an air-handling assembly Formulation of a hysteretic restoring force model. application to vibration isolation Global behavior of a nonlinear quasiperiodic mathieu equation 27(1) 2002 Zaki K. Noah S. Rajagopal KR. Srinivasa AR. Yu P. McGee CG. Adams DE. Al Majid A. Dufour R. Zounes RS. Rand RH. Nonlinear Dynamics 107 185 197 Nonlinear dynamics of oating cranes Type-i intermittency and crisis-induced intermittency in a semiconductor laser under injection current modulation Optimal control of populations of competing species 27(2) 2002 Ellermann K. Kreuzer E. Markiewicz M. Manra EF. Caldas IL. Viana RL. Kalinowski HJ. Crespo LG. Sun JQ. Nonlinear Dynamics 211 237 255 271 295 Quasi-periodic solutions and stability for a weakly damped nonlinear quasiperiodic mathieu equation On the proper form of the amplitude modulation equations for resonant systems Pendulation reduction in boom cranes using cable length manipulation Common features of the onset of the persistent chaos in nonlinear oscillators: a phenomenological approach Robust feedback stabilization of limit cycles in pwm dc-dc converters Proceedings of the Royal Society of London Series AMathematical, Physical and Engineering Sciences 255 271 283 299 319 339 359 381 On the stability of the upside-down pendulum with damping Solution of the generalized riemann problem for advection-reaction equations Secondary boundary layer and wall shear for fully developed ow in curved pipes Non-convex potentials and microstructures in nite-strain plasticity Conserved currents, superpotentials and cosmological perturbations Vibrations of a shallow cable with a viscous damper A framework for perturbations and stability of dierentially rotating stars Yoe-type moving crack in a functionally graded piezoelectric material 27(3) 2002 Guennoun K. Houssni M. Belhaq M. Luongo A. Di Egidio A. Paolone A. Abdel-Rahman EM. Nayfeh AH. Szemplinska-Stupnicka W. Tyrkiel E. Fang CC. Abed EH. 458(2018) 2002 Bartuccelli MV. Gentile G. Georgiou KV. Toro EF. Titarev VA. Dey S. Carstensen C. Hackl K. Mielke A. Petrov AN. Katz J. Krenk S. Nielsen SRK. Beyer HR. Li CY. Weng GJ. 401 429 451 473 489 Numerical solution for diraction of an electromagnetic wave by slits in a perfectly conducting screen Multi-dimensional solutions of space-time-fractional diusion equations Pauli's theorem and quantum canonical pairs: the consistency of a bounded, selfadjoint time operator canonically conjugate to a hamiltonian with non-empty point spectrum Unsteady pressure elds which precede the launch of free-surface liquid jets A vector potential and exact ux through surfaces using lagrange and stokes stream functions Hanyga A. Galapon EA. Cooker MJ. Steward DR. Quarterly Journal of Mechanics & Applied Mathematics 1 17 29 49 69 93 109 127 141 Courant's nodal line theorem and its discrete counterparts Some aspects of nite amplitude transverse waves in a compressible hyperelastic solid The cantilever strip plate of varying thickness and the centre of shear Interference and turning of in-parallel wakes Hysteresis in the stress-cycling of bars undergoing solid-solid phase transitions Wave reection and transmission from anisotropic layers through riccati equations Small-amplitude inhomogeneous plane waves in a deformed mooney-rivlin material On the non-existence of surface waves trapped by submerged obstructions having exterior cusp points Two asymptotic forms of the rotational solution for wave propagation inside viscous channels with transpiring walls 33 Nye JF. 55(Part 1) 2002 Gladwell GML. Haddow JB. Erbay HA. Gregory RD. Gu CC. Wan FYM. Smith FT. Knowles JK. Caviglia G. Morro A. Destrade M. Motygin V. Majdalani J. Rienstra SW. Quarterly of Applied Mathematics 1 11 37 75 87 99 111 131 153 183 195 A note on the persistence of leading n-waves of tsunami Theory of exact solutions for the evolution of a uid annulus in a rotating heleshaw cell A geometric evolution problem Convex polyhedra quantum billiards in r-n "forbidden" planes for rayleigh waves On derivative of energy functional for elastic bodies with cracks and unilateral conditions Stabilization of the korteweg-de vries equation with localized damping A mathematical analysis of electrical discharges Maximum recoverable work, minimum free energy and state space in linear viscoelasticity Existence and uniqueness of solutions of smoluchowski's coagulation equation with source terms Uniqueness and construction of solution for the nonlinear elastodiusion problem 60(1) 2002 Kovalyov M. Crowdy D. Bergwall A. Libo RL. Kuznetsov SV. Khludnev AM. Ohtsuka K. Sokolowski J. Menzala GP. Vasconcellos CF. Zuazua E. Severin F. Nouri A. Gentili G. Shirvani M. Van Roessel HJ. Markensco X. Rheologica Acta 1 10 25 35 45 55 61 77 87 93 Gelation study of high processability and high reliability ternary systems based on benzoxazine, epoxy, and phenolic resins for an application as electronic packaging materials Eect of maleic anhydride content on the rheology and phase behavior of poly(styrene-co-maleic anhydride)/poly(methyl methacrylate) blends Surfactant-induced eects on turbulent swirling ows Shear-banding structure orientated in the vorticity direction observed for equimolar micellar solution Rheology and ow-birefringence from viscoelastic polymer-clay solutions The eect of mixing particles of dierent size on the electrorheological response under steady shear ow The normal stress behaviour of suspensions with viscoelastic matrix uids Quantitative rheological evaluation of phase inversion in two-phase polymer blends with cocontinuous morphology Coupling between ow and diusion at polymer/polymer interfaces: large amplitude oscillatory shear experiments A network model with free-strand dynamics for polymer melts 41(1-2) 2002 Rimdusit S. Ishida H. Chopra D. Kontopoulou M. Vlassopoulos D. Hatzikiriakos SG. Arora K. Sureshkumar R. Scheiner MP. Piper JL. Fischer P. Wheeler EK. Fuller GG. Schmidt G. Nakatani AI. Han CC. See H. Kawai A. Ikazaki F. Mall-Gleissle SE. Gleissle W. McKinley GH. Buggisch H. Steinmann S. Gronski W. Friedrich C. Qiu H. Bousmina M. Dealy JM. Seimenis M. Wedgewood LE. 34 103 114 134 Van gurp-palmen plot ii - classication of long chain branched polymers by their topology Birefringence measurements on polymer melts in an axisymmetric ow cell 162 Extrusion of pastes with a piston extruder for the determination of the local solid and uid concentration, the local porosity and saturation and displacement proles by means of nmr imaging Three-dimensional viscoelastic simulation of coextrusion process: comparison with experimental data Small and large strain rheology of wheat gluten 173 The rheology of bread dough made from four commercial ours 180 Viscoelastic properties of pig kidney in shear, experimental results and modelling 144 Trinkle S. Walter P. Friedrich C. Harrison P. Janssen LJP. Navez VP. Peters GWM. Baaijens FPT. Gotz J. Kreibich W. Peciar M. Sunwoo KB. Park SJ. Lee SJ. Ahn KH. Uthayakumaran S. Newberry M. Phan-Thien N. Tanner R. Keentok M. Newberry MP. Gras P. Bekes F. Tanner RI. Nasseri S. Bilston LE. Phan-Thien N. Studies in Applied Mathematics 1 7 29 39 65 77 89 105 123 145 Research contributions of david j. benney On transition to turbulence and synthesis of alternative approaches From disorder to order - august 2000 Wave turbulence is almost always intermittent at either small or large scales Slow passage through the nonhyperbolic homoclinic orbit of the saddle-center hamiltonian bifurcation Long-wave instability in a three-layer stratied shear ow Subcritical rossby waves in zonal shear ows with nonlinear critical layers Resonant triads involving a nondispersive wave Resonant wave interaction with random forcing and dissipation Eigenfunctions of linearized integrable equations expanded around an arbitrary solution 108(1) 2002 Ablowitz MJ. Akylas TR. Lin CC. Lin CC. Malkus WVR. Newell AC. Diminnie DC. Haberman R. Grimshaw R. Skyrnnikov Y. Maslowe SA. Clarke SR. Rosales RR. Tabak EG. Turner CV. Milewski PA. Tabak EG. Vanden-Eijnden E. Yang JK. Studies in Applied Mathematics 161 187 217 A uniformly valid asymptotic approach to the inviscid-viscous interaction theory Asymptotic expansions of generalized stieltjes transforms of algebraically decaying functions Proof of the stokes conjecture in the theory of surface waves 108(2) 2002 Turkyilmazoglu M. Ruban AI. Lopez JL. Ferreira C. Plotnikov PI. Thin-Walled Structures 215 225 239 263 283 297 Analytical solution for forced vibration of a simply-supported v-shaped folded plate roof The suitability of round clinching tools for high strength structural steel Eect of imperfections on numerical simulation of instability behaviour of coldformed steel members Design procedure for stiened water-lled steel conical tanks Periodicity in the response of nonlinear plate, under moving mass Optimization of open cross section of the thin-walled beam with at web and circular ange 40(3) 2002 Lai YM. Yu WB. Varis JP. Dubina D. Ungureanu V. El Damatty AA. Marroquin E. Shadnam MR. Rofooei FR. Mod M. Mehri B. Magnucki K. Zeitschrift fur Angewandte Mathematik und Mechanik 75 89 101 115 125 137 142 On the asymptotic analysis of discontinuous systems Low-frequency dispersion-function factorization and classication of p-sv modes by wavenumber limits An approximate newton-like coupling of subsystems Inltration through deformable porous media A stage structure model for the growth of a population involving switching and cooperation Low-frequency penetration of a plane elastic wave through the periodic array of interface cracks A note on the free convection from curved surfaces 82(2) 2002 Fidlin A. Ivansson S. Menck J. Ambrosi D. Khan QJA. Krishnan EV. Al-Lawatia MA. Ciarletta M. Alexandrov VM. Sumbatyan MA. Magyari E. Pop I. Keller B. 35 Zeitschrift fur Angewandte Mathematik und Mechanik 147 159 167 177 191 201 207 211 On criteria for asymptotic stability of dierential-algebraic equations Complex fractional programming involving generalized quasi/pseudo convex functions Fluid ow with dynamic contact angle: numerical simulation All about carnot ow Spectrum modication for gyroscopic systems On creep rupture of rectangular plates Bobillier formula as a fundamental law in planar motion The role of induced air shear on the development of a conducting uid lm over a rough spinning disk in the presence of a transverse magnetic eld 82(3) 2002 Stykel T. Lai HC. Liu JC. Dorer W. Goncharova O. Kroner D. Forster K. Datta BN. Ram YM. Sarkissian DR. Bodnar A. Chrzanowski M. Fayet M. Usha R. Uma B. Zeitschrift fur Angewandte Mathematik und Physik 1 12 20 35 48 58 73 90 103 123 147 160 167 Some blow-up results for a generalized ginzburg-landau equation Thermal ow through a porous radiant of low conductivity Spectral stability of small-amplitude shock proles for dissipative symmetric hyperbolic-parabolic systems Axisymmetric wake and jet solutions in decelerating streams Natural convection of uid with variable viscosity from a heated vertical wavy surface Boundary slip phenomena in a binary gas mixture Well-posedness of the dirichlet problem in non-elliptic isotropic elasticity Elastostatic inverse formulation Travelling fronts for the kpp equation with spatio-temporal delay Computation of lyapunov characteristic exponents for continuous dynamical systems Blow-up in a reactive-diusive medium with a moving heat source The bailey criterion: statistical derivation and applications to interpretations of durability tests and chemical kinetics The motion of two axi-symmetric rigid bodies with friction coupling 53(1) 2002 Aassila M. Polisevski D. Humphreys J. Zumbrun K. Barker J. Wilks G. Hossain MA. Kabir S. Rees DAS. Ivchenko IN. Loyalka SK. Tompson RV. Ernst E. Xu W. Genin J. Ashwin P. Bartuccelli MV. Bridges TJ. Gourley SA. Udwadia FE. von Bremen HF. Kirk CM. Olmstead WE. Freed AD. Leonov AI. Wilms EV. Cohen H.